Professor Catherine Greenhill

Professor Catherine Greenhill

Professor
  • D.Phil., University of Oxford, 1996.
  • M.Sc. (Research) in Combinatorics, University of Queensland, 1992.
  • B.Sc. (Hons) in Pure Mathematics, University of Queensland, 1991.
Science
School of Mathematics & Statistics

I started my academic career as an undergraduate at the University of Queensland, before obtaining my doctorate from the University of Oxford (1992). I held postdoctoral positions at the University of Leeds and at the University of Melbourne, before joining UNSW in 2002.  Today I am a Professor and head of the Combinatorics group in the School of Mathematics and Statistics, UNSW Sydney. My research interests lie in asymptotic, probabilistic and algorithmic combinatorics.  I was elected as a Fellow of the Australian Academy of Science in 2022. My work lies at the interface between discrete mathematics, theoretical computer science and probability, and has been applied by researchers in various areas including physics, computer science and statistics.

Phone
9385 7105
Location
School of Mathematics and Statistics UNSW Sydney NSW 2052, AUSTRALIA The Red Centre Room 5105
  • Books | 2002
    Greenhill CS, 2002, Proceedings of FPSAC 2002, Brak R; Foda O; Greenhill C; Guttmann T; Owczarek A, (eds.), The University of Melbourne, Melbourne
  • Book Chapters | 2021
    Book Chapters | 2013
    Bright DA; Greenhill C; Levenkova N, 2013, 'Dismantling criminal networks: Can node attributes play a role?', in Crime and Networks, pp. 148 - 162, http://dx.doi.org/10.4324/9781315885018-16
    Book Chapters | 2013
    Bright DA; Greenhill C; Levenkova N, 2013, 'Dismantling criminal networks: can node attributes play a role?', in Morselli C (ed.), Crime and Networks, Routledge, pp. 148 - 162, http://www.routledge.com/
    Book Chapters | 1999
    Dyer M; Greenhill C, 1999, 'Random walks on combinatorial objects', in Lamb JD; Preece DA; Preece DA (ed.), Surveys in Combinatorics, Cambridge University Press, Cambridge, pp. 101 - 136
  • Journal articles | 2024
    Pitman AJ; Saribatir E; Greenhill C; Green S; Pitman SJ; Fiedler T, 2024, 'Linking physical climate risk with mandatory business risk disclosure requirements', Environmental Research Letters, 19, http://dx.doi.org/10.1088/1748-9326/ad4377
    Journal articles | 2023
    Greenhill C; Mans B; Pourmiri A, 2023, 'Balanced allocation on hypergraphs', Journal of Computer and System Sciences, 138, http://dx.doi.org/10.1016/j.jcss.2023.05.004
    Journal articles | 2022
    Ayre P; Coja-Oghlan A; Greenhill C, 2022, 'Lower Bounds on the Chromatic Number of Random Graphs', Combinatorica, 42, pp. 617 - 658, http://dx.doi.org/10.1007/s00493-021-4236-z
    Journal articles | 2022
    Erdős PL; Greenhill C; Mezei TR; Miklós I; Soltész D; Soukup L, 2022, 'The mixing time of switch Markov chains: A unified approach', European Journal of Combinatorics, 99, http://dx.doi.org/10.1016/j.ejc.2021.103421
    Journal articles | 2022
    Greenhill C; Isaev M; Makai T; McKay BD, 2022, 'Degree sequences of sufficiently dense random uniform hypergraphs', COMBINATORICS PROBABILITY & COMPUTING, http://dx.doi.org/10.1017/S0963548322000190
    Journal articles | 2022
    Greenhill C, 2022, 'Spanning trees in random regular uniform hypergraphs', Combinatorics, Probability and Computing, 31, pp. 29 - 53, http://dx.doi.org/10.1017/S0963548321000158
    Journal articles | 2021
    Aldosari HS; Greenhill C, 2021, 'The average number of spanning hypertrees in sparse uniform hypergraphs', Discrete Mathematics, 344, pp. 112192, http://dx.doi.org/10.1016/j.disc.2020.112192
    Journal articles | 2021
    Chen C; Greenhill C, 2021, 'Threshold functions for substructures in random subsets of finite vector spaces', JOURNAL OF COMBINATORICS, 12, pp. 157 - 183, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000605448000006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Journal articles | 2021
    Dyer M; Greenhill C; Kleer P; Ross J; Stougie L, 2021, 'Sampling hypergraphs with given degrees', Discrete Mathematics, 344, pp. 112566, http://dx.doi.org/10.1016/j.disc.2021.112566
    Journal articles | 2021
    Dyer M; Greenhill C; Müller H, 2021, 'Counting independent sets in graphs with bounded bipartite pathwidth', Random Structures and Algorithms, 59, pp. 204 - 237, http://dx.doi.org/10.1002/rsa.21003
    Journal articles | 2021
    Gao P; Greenhill C, 2021, 'Mixing time of the switch Markov chain and stable degree sequences', Discrete Applied Mathematics, 291, pp. 143 - 162, http://dx.doi.org/10.1016/j.dam.2020.12.004
    Journal articles | 2021
    Greenhill C; Isaev M; McKay BD, 2021, 'Subgraph counts for dense random graphs with specified degrees', Combinatorics Probability and Computing, 30, pp. 460 - 497, http://dx.doi.org/10.1017/S0963548320000498
    Journal articles | 2020
    Altman D; Greenhill C; Isaev M; Ramadurai R, 2020, 'A threshold result for loose Hamiltonicity in random regular uniform hypergraphs', Journal of Combinatorial Theory. Series B, 142, pp. 307 - 373, http://dx.doi.org/10.1016/j.jctb.2019.11.001
    Journal articles | 2019
    Aldosari HS; Greenhill C, 2019, 'Enumerating sparse uniform hypergraphs with given degree sequence and forbidden edges', European Journal of Combinatorics, 77, pp. 68 - 77, http://dx.doi.org/10.1016/j.ejc.2018.11.002
    Journal articles | 2019
    Ayre P; Coja-Oghlan A; Greenhill C, 2019, 'Hypergraph coloring up to condensation', Random Structures and Algorithms, 54, pp. 615 - 652, http://dx.doi.org/10.1002/rsa.20824
    Journal articles | 2019
    Ayre P; Greenhill C, 2019, 'Rigid colorings of hypergraphs and contiguity', SIAM Journal on Discrete Mathematics, 33, pp. 1575 - 1606, http://dx.doi.org/10.1137/18M1207211
    Journal articles | 2019
    Cooper C; Dyer M; Greenhill C; Handley A, 2019, 'The flip Markov chain for connected regular graphs', Discrete Applied Mathematics, 254, pp. 56 - 79, http://dx.doi.org/10.1016/j.dam.2018.06.019
    Journal articles | 2019
    Cooper C; Dyer M; Greenhill C, 2019, 'Triangle-creation processes on cubic graphs', , http://arxiv.org/abs/1905.04490v1
    Journal articles | 2019
    Dyer M; Greenhill C; Müller H, 2019, 'Counting Independent Sets in Graphs with Bounded Bipartite Pathwidth', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 11789 LNCS, pp. 298 - 310, http://dx.doi.org/10.1007/978-3-030-30786-8_23
    Journal articles | 2019
    Erdős PL; Greenhill CS; Mezei TR; Miklós I; Soltész D; Soukup L, 2019, 'Mixing time of the swap Markov chain and P-stability', Acta Mathematica Universitatis Comenianae, 88, pp. 659 - 665, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000484349000047&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Journal articles | 2019
    Gao P; Greenhill C, 2019, 'Uniform generation of spanning regular subgraphs of a dense graph', Electronic Journal of Combinatorics, 26, http://dx.doi.org/10.37236/8251
    Journal articles | 2018
    Greenhill C; Sfragara M, 2018, 'The switch Markov chain for sampling irregular graphs and digraphs', Theoretical Computer Science, 719, pp. 1 - 20, http://dx.doi.org/10.1016/j.tcs.2017.11.010
    Journal articles | 2017
    Bright D; Greenhill C; Britz T; Ritter A; Morselli C, 2017, 'Criminal network vulnerabilities and adaptations', Global Crime, 18, pp. 424 - 441, http://dx.doi.org/10.1080/17440572.2017.1377614
    Journal articles | 2017
    Greenhill C; Isaev M; Kwan M; McKay BD, 2017, 'The average number of spanning trees in sparse graphs with given degrees', European Journal of Combinatorics, 63, pp. 6 - 25, http://dx.doi.org/10.1016/j.ejc.2017.02.003
    Journal articles | 2016
    Blinovsky V; Greenhill C, 2016, 'Asymptotic enumeration of sparse uniform hypergraphs with given degrees', European Journal of Combinatorics, 51, pp. 287 - 296, http://dx.doi.org/10.1016/j.ejc.2015.06.004
    Journal articles | 2016
    Blinovsky V; Greenhill C, 2016, 'Asymptotic enumeration of sparse uniform linear hypergraphs with given degrees', ELECTRONIC JOURNAL OF COMBINATORICS, 23, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000385228300003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Journal articles | 2015
    Bright DA; Greenhill C; Reynolds M; Ritter A; Morselli C, 2015, 'The Use of Actor-Level Attributes and Centrality Measures to Identify Key Actors: A Case Study of an Australian Drug Trafficking Network', Journal of Contemporary Criminal Justice, 31, pp. 262 - 278, http://dx.doi.org/10.1177/1043986214553378
    Journal articles | 2015
    Bright DA; Greenhill C; Ritter A; Morselli C, 2015, 'Networks within networks: using multiple link types to examine network structure and identify key actors in a drug trafficking operation', Global Crime, 16, pp. 219 - 237, http://dx.doi.org/10.1080/17440572.2015.1039164
    Journal articles | 2015
    Dyer M; Frieze A; Greenhill C, 2015, 'On the chromatic number of a random hypergraph', Journal of Combinatorial Theory. Series B, 113, pp. 68 - 122, http://dx.doi.org/10.1016/j.jctb.2015.01.002
    Journal articles | 2014
    Bordewich M; Greenhill C; Patel V, 2014, 'Mixing of the Glauber dynamics for the ferromagnetic Potts model', Random Structures & Algorithms, pp. n/a - n/a, http://dx.doi.org/10.1002/rsa.20569
    Journal articles | 2014
    Dyer M; Greenhill C; Ullrich M, 2014, 'Structure and eigenvalues of heat-bath Markov chains', Linear Algebra and Its Applications, 454, pp. 57 - 71, http://dx.doi.org/10.1016/j.laa.2014.04.018
    Journal articles | 2014
    Greenhill C; Kwan M; Wind D, 2014, 'On the number of spanning trees in random regular graphs', Electronic Journal of Combinatorics, 21, http://dx.doi.org/10.37236/3752
    Journal articles | 2013
    Greenhill C; Mckay BD, 2013, 'Asymptotic enumeration of sparse multigraphs with given degrees', SIAM Journal on Discrete Mathematics, 27, pp. 2064 - 2089, http://dx.doi.org/10.1137/130913419
    Journal articles | 2012
    Cooper C; Dyer M; Greenhill C, 2012, 'Corrigendum: Sampling regular graphs and a peer-to-peer network', Corrigendum: Sampling regular graphs and a peer-to-peer network, http://arxiv.org/abs/1203.6111v1
    Journal articles | 2012
    Greenhill CS; McKay BD, 2012, 'Counting loopy graphs with given degrees', Linear Algebra and its Applications, 436, pp. 901 - 926, http://dx.doi.org/10.1016/j.laa.2011.03.052
    Journal articles | 2011
    Greenhill CS, 2011, 'A polynomial bound on the mixing time of a Markov chain for sampling regular directed graphs', Electronic Journal of Combinatorics, 18, pp. #234 (49pp)
    Journal articles | 2010
    Canfield ER; Gao Z; Greenhill CS; McKay BD; Robinson RW, 2010, 'Asymptotic enumeration of correlation-immune boolean functions', Cryptography and Communications, 2, pp. 111 - 126
    Journal articles | 2010
    Greenhill CS; Janson S; Rucinski A, 2010, 'On the number of perfect matchings in random lifts', Combinatorics Probability and Computing, 19, pp. 791 - 817, http://dx.doi.org/10.1017/S0963548309990654
    Journal articles | 2009
    Greenhill CS; McKay BD, 2009, 'Random dense bipartite graphs and directed graphs with specified degrees', Random Structures and Algorithms, 35, pp. 222 - 249
    Journal articles | 2008
    Canfield E; Greenhill CS; McKay BD, 2008, 'Asymptoic enumeration of dense 0-1 matrices with specified line sums', Journal of Combinatorial Theory Series A, 115, pp. 32 - 66
    Journal articles | 2008
    Cavenagh N; Greenhill CS; Wanless IM, 2008, 'The cycle structure of two rows in a random Latin square', Random Structures and Algorithms, 33, pp. 286 - 309
    Journal articles | 2008
    Greenhill CS; Holt F; Wormald NC, 2008, 'Expansion properties of a random regular graph after random vertex deletions', European Journal of Combinatorics, 29, pp. 1139 - 1150, http://dx.doi.org/10.1016/j.ejc.2007.06.021
    Journal articles | 2008
    Greenhill CS; McKay BD, 2008, 'Asymptotic enumeration of sparse nonnegative integer matrices with specified row and column sums', Advances in Applied Mathematics, 41, pp. 459 - 481
    Journal articles | 2007
    Cooper C; Dyer M; Greenhill CS, 2007, 'Sampling regular graphs and a peer-to-peer network', Combinatorics Probability and Computing, 16, pp. 557 - 593
    Journal articles | 2006
    Gerke S; Greenhill CS; Wormald NC, 2006, 'The generalized acyclic edge chromatic number of random regular graphs', Journal of Graph Theory, 53, pp. 101 - 125
    Journal articles | 2006
    Greenhill CS; McKay BD; Wang XJ, 2006, 'Asymptotic enumeration of sparse 0-1 matrices with irregular row and column sums', Journal of Combinatorial Theory Series A, 113, pp. 291 - 324
    Journal articles | 2006
    Greenhill CS; Rucinski A, 2006, 'Neighbour-distinguishing edge colourings of random regular graphs', Electronic Journal of Combinatorics, 13, pp. 1 - 12
    Journal articles | 2005
    Brinkmann G; Greenberg S; Greenhill CS; McKay BD; Thomas R; Wollan P, 2005, 'Generation of simple quadrangulations of the sphere', Discrete Mathematics, 305, pp. 33 - 54
    Journal articles | 2005
    Cooper C; Dyer M; Greenhill C, 2005, 'Sampling regular graphs and a peer-to-peer network', Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 980 - 988
    Journal articles | 2005
    Greenhill CS; Pikhurko O, 2005, 'Bounds on the generalised acyclic chronatic numbers of bounded degree graphs', Graphs and Combinatorics, 21, pp. 407 - 419, http://dx.doi.org/10.1007/s00373-005-0635-y
    Journal articles | 2004
    Greenhill C; Kim JH; Wormald NC, 2004, 'Hamiltonian decompositions of random bipartite regular graphs', Journal of Combinatorial Theory. Series B, 90, pp. 195 - 222, http://dx.doi.org/10.1016/j.jctb.2003.07.001
    Journal articles | 2004
    Greenhill CS; Dyer M, 2004, 'Corrigendum: The complexity of counting graph homomorphisms (Vol 17, pg 260, 2000)', Random Structures and Algorithms, 25, pp. 346 - 352
    Journal articles | 2004
    Greenhill CS; Rucinski A; Wormald NC, 2004, 'Random hypergraph processes with degree restrictions', Graphs and Combinatorics, 20, pp. 319 - 332, http://dx.doi.org/10.1007/s00373-004-0571-2
    Journal articles | 2003
    Dyer M; Goldberg LA; Greenhill C; Jerrum M, 2003, 'The relative complexity of approximate counting problems', Algorithmica (New York), 38, pp. 471 - 500, http://dx.doi.org/10.1007/s00453-003-1073-y
    Journal articles | 2003
    Greenhill C; Ruciski A; Wormald N, 2003, 'Connectedness of the Degree Bounded Star Process', Combinatorics, Probability and Computing, 12, pp. 269 - 283, http://dx.doi.org/10.1017/S0963548302005357
    Journal articles | 2002
    Dyer M; Goldberg LA; Greenhill C; Istrate G; Jerrum M, 2002, 'Convergence of the iterated prisoner's dilemma game', Combinatorics Probability and Computing, 11, pp. 135 - 147, http://dx.doi.org/10.1017/S096354830100503X
    Journal articles | 2002
    Dyer M; Greenhill C; Molloy M, 2002, 'Very Rapid Mixing of the Glauber Dynamics for Proper Colorings on Bounded-Degree Graphs', Random Structures and Algorithms, 20, pp. 98 - 114, http://dx.doi.org/10.1002/rsa.10020
    Journal articles | 2002
    Greenhill C; Janson S; Kim J; Wormald N, 2002, 'Permutation Pseudographs and Contiguity', Combinatorics, Probability and Computing, 11, http://dx.doi.org/10.1017/S0963548301005065
    Journal articles | 2000
    Dyer M; Goldberg LA; Greenhill C; Jerrum M; Mitzenmacher M, 2000, 'Extension of path coupling and its application to the Glauber dynamics for graph colourings', Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 616 - 624
    Journal articles | 2000
    Dyer M; Greenhill C, 2000, 'Complexity of counting graph homomorphisms', Proceedings of the Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 246 - 255
    Journal articles | 2000
    Dyer M; Greenhill C, 2000, 'On Markov Chains for Independent Sets', Journal of Algorithms, 35, pp. 17 - 49, http://dx.doi.org/10.1006/jagm.1999.1071
    Journal articles | 2000
    Dyer M; Greenhill C, 2000, 'Polynomial-time counting and sampling of two-rowed contingency tables', Theoretical Computer Science, 246, pp. 265 - 278, http://dx.doi.org/10.1016/S0304-3975(99)00136-X
    Journal articles | 2000
    Dyer M; Greenhill C, 2000, 'The complexity of counting graph homomorphisms', Random Structures and Algorithms, 17, pp. 260 - 289, http://dx.doi.org/10.1002/1098-2418(200010/12)17:3/4<260::aid-rsa5>3.0.co;2-w
    Journal articles | 2000
    Dyer M; Leslie Goldberg A; Greenhill C; Jerrum M; Mitzenmacheru M, 2000, 'An extension of path coupling and its application to the glauber dynamics for graph colorings', SIAM Journal on Computing, 30, pp. 1962 - 1975, http://dx.doi.org/10.1137/s0097539700372708
    Journal articles | 2000
    Greenhill C, 2000, 'The complexity of counting colourings and independent sets in sparse graphs and hypergraphs', Computational Complexity, 9, pp. 52 - 72, http://dx.doi.org/10.1007/PL00001601
    Journal articles | 1999
    Bubley R; Dyer M; Greenhill C; Jerrum M, 1999, 'On approximately counting colorings of small degree graphs', SIAM Journal on Computing, 29, pp. 387 - 400, http://dx.doi.org/10.1137/S0097539798338175
    Journal articles | 1999
    Greenhill C, 1999, 'An algorithm for recognising the exterior square of a matrix', Linear and Multilinear Algebra, 46, pp. 213 - 244, http://dx.doi.org/10.1080/03081089908818615
    Journal articles | 1998
    Dyer M; Greenhill C, 1998, 'A genuinely polynomial-time algorithm for sampling two-rowed contingency tables', , pp. 339 - 350, http://dx.doi.org/10.1007/BFb0055065
    Journal articles | 1998
    Dyer M; Greenhill C, 1998, 'A more rapidly mixing Markov chain for graph colorings', Random Structures and Algorithms, 13, pp. 285 - 317, http://dx.doi.org/10.1002/(sici)1098-2418(199810/12)13:3/4<285::aid-rsa6>3.0.co;2-r
    Journal articles | 1995
    Greenhill CS; Street AP, 1995, 'Smallest defining sets of some small t-designs and relations to the Petersen graph', Utilitas Mathematica, 48, pp. 5 - 31
    Journal articles | 1995
    Greenhill CS, 1995, 'Theoretical and Experimental Comparison of Efficiency of Finite Field Extensions', Journal of Symbolic Computation, 20, pp. 419 - 429, http://dx.doi.org/10.1006/jsco.1995.1057
    Journal articles | 1993
    Greenhill CS, 1993, 'An algorithm for finding smallest defining sets of t-designs', Journal of Combinatorial Mathematics and Combinatorial Computing, 14, pp. 39 - 60
  • Working Papers | 2021
    Greenhill C; Isaev M; Makai T; McKay BD, 2021, Degree sequences of sufficiently dense random uniform hypergraphs, http://dx.doi.org, http://arxiv.org/abs/2106.08100v2
  • Preprints | 2023
    Cooper C; Dyer M; Greenhill C, 2023, A triangle process on graphs with given degree sequence, , http://arxiv.org/abs/2301.08499v1
    Preprints | 2023
    Delcourt M; Greenhill C; Isaev M; Lidický B; Postle L, 2023, Decomposing random regular graphs into stars, , http://arxiv.org/abs/2308.16037v1
    Preprints | 2022
    Greenhill C, 2022, Generating graphs randomly, , http://arxiv.org/abs/2201.04888v1
    Conference Papers | 2021
    Cooper C; Dyer M; Greenhill C, 2021, 'A Triangle Process on Regular Graphs', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Springer International Publishing, pp. 310 - 323, http://dx.doi.org/10.1007/978-3-030-79987-8_22
    Preprints | 2020
    Dyer M; Greenhill C; Kleer P; Ross J; Stougie L, 2020, Sampling hypergraphs with given degrees, , http://dx.doi.org/10.48550/arxiv.2006.12021
    Conference Papers | 2020
    Greenhill C; Mans B; Pourmiri A, 2020, 'Balanced allocation on dynamic hypergraphs', in Leibniz International Proceedings in Informatics, LIPIcs, http://dx.doi.org/10.4230/LIPIcs.APPROX/RANDOM.2020.11
    Preprints | 2019
    Aldosari HS; Greenhill C, 2019, The average number of spanning hypertrees in sparse uniform hypergraphs, , http://dx.doi.org/10.48550/arxiv.1907.04993
    Preprints | 2019
    Erdős PL; Greenhill C; Mezei TR; Miklós I; Soltész D; Soukup L, 2019, The mixing time of the switch Markov chains: a unified approach, , http://dx.doi.org/10.48550/arxiv.1903.06600
    Preprints | 2018
    Aldosari HS; Greenhill C, 2018, Enumerating sparse uniform hypergraphs with given degree sequence and forbidden edges, , http://dx.doi.org/10.48550/arxiv.1805.04991
    Preprints | 2016
    Altman D; Greenhill C; Isaev M; Ramadurai R, 2016, A threshold result for loose Hamiltonicity in random regular uniform hypergraphs, , http://dx.doi.org/10.48550/arxiv.1611.09423
    Preprints | 2015
    Ayre P; Coja-Oghlan A; Greenhill C, 2015, Hypergraph coloring up to condensation, , http://dx.doi.org/10.48550/arxiv.1508.01841
    Conference Papers | 2015
    Greenhill CS, 2015, 'The switch Markov chain for sampling irregular graphs', in The 26th Annual ACM-SIAM Symposium on Discrete Algorithms, ACM-SIAM, San Diego, CA, USA, pp. 1565 - 1572, presented at 26th annual ACM-SIAM Symposium on Discrete Algorithms, San Diego, CA, USA, 04 January 2015 - 06 January 2015, http://dx.doi.org/10.1137/1.9781611973730.103
    Preprints | 2014
    Blinovsky V; Greenhill C, 2014, Asymptotic enumeration of sparse uniform linear hypergraphs with given degrees, , http://dx.doi.org/10.48550/arxiv.1409.1314
    Preprints | 2013
    Blinovsky V; Greenhill C, 2013, Asymptotic enumeration of sparse uniform hypergraphs with given degrees, , http://dx.doi.org/10.48550/arxiv.1306.2012
    Conference Papers | 2000
    Dyer M; Goldberg LA; Greenhill C; Jerrum M, 2000, 'On the relative complexity of approximate counting problems', in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), pp. 108 - 119, http://dx.doi.org/10.1007/3-540-44436-x_12
    Conference Papers | 2000
    Dyer M; Greenhill C, 2000, 'The complexity of counting graph homomorphisms (extended abstract)', in PROCEEDINGS OF THE ELEVENTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, SIAM, CA, SAN FRANCISCO, pp. 246 - 255, presented at 11th Annual ACM/SIAM Symposium on Discrete Algorithms, CA, SAN FRANCISCO, 09 January 2000 - 11 January 2000, https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000085602800035&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1
    Conference Papers | 2000
    Dyer M; Greenhill CS, 2000, 'An extension of path coupling and its application to the Glauber dynamics for graph colourings (Extended abstract)', in PROCEEDINGS OF THE ELEVENTH ANNUAL ACM-SIAM SYMPOSIUM ON DISCRETE ALGORITHMS, SIAM, New York-Philadelphia, pp. 616 - 624, presented at 11th Annual ACM-SIAM Symposium on Discrete Algorithms, SAN FRANCISCO, CA, 09 January 2000 - 11 January 2000, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000085602800082&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a
    Conference Papers | 1998
    Bubley R; Dyer M; Greenhill CS, 1998, 'Beating the $2\Delta$ bound for approximately counting colourings: a computer-assisted proof of rapid mixing', in The 9th Annual ACM-SIAM Symposium on Discrete Algorithms, New York-Philidelphia, pp. 355 - 363, 25 January 1998 - 27 January 1998

  • ARC Discovery Grant 2019 - 2021, C.S. Greenhill, B.D. McKay (ANU) and M. Isaev (Monash), Hypergraph models for complex discrete systems.
  • ARC Discovery Grant 2014 – 2016, C.S. Greenhill and B.D. McKay (ANU), A new model for random discrete structures: distributions, sampling and counting.
  • ARC Discovery Grant 2012 – 2014, I.M. Wanless (Monash), C.S. Greenhill and R. Aharoni (Technion), Extremal problems in hypergraph matchings.
  • ARC Discovery Grant 2012 – 2013, D.A. Bright, C.S. Greenhill, A. Ritter and C. Morselli (Montreal), Illicit drug trafficking: the structure of illicit networks and implications for resilience and vulnerability.

  • I was elected as a Fellow of the Australian Academy of Science in 2022.
  • The Australian Academy of Science awarded the 2015 Christopher Heyde Medal in Pure Mathematics.
  • In 2013 I held the June Griffith Fellowship for Academic Women in Leadership, awarded by the Faculty of Science, UNSW.
  • I was awarded the 2010 Hall Medal by the Institute of Combinatorics and its Applications. This is an international mid-career medal for research in combinatorics.

The study of random combinatorial objects, such as random graphs, is an attempt to discover what a "typical" graph with certain properties might look like (for instance, a given number of vertices and edges, or a given number of vertices and every vertex having a fixed degree). This work involves a mixture of combinatorial and probabilistic arguments, and the results obtained are asymptotic, meaning that they hold in the limit as the number of vertices of the graph tends to infinity.

A related area is asymptotic enumeration of various kinds of graphs. This means finding a formula for the number of graphs of interest which is closer and closer to the truth as the number of vertices tends to infinity. For sparse graphs the methods are combinatorial and often involve a probabilistic approach using switchings. For dense graphs the approach is quite different: we want to to know a particular coefficient of the generating function and proceed using complex analysis, evaluating integrals using the saddle-point method.

I am also interested in the design and analysis of randomized algorithms for graphs and other combinatorial structures, particularly Markov chain Monte Carlo algorithms for approximate sampling and/or counting. Here a Markov chain is designed with a given stationary distribution, for instance the uniform distribution on the set of all graphs with a given degree sequence. The aim is to prove that the Markov chain converges rapidly (i.e. in polynomial time) to this distribution.

Conference committees (recent)

  • I was Director of 42ACCMCC, the 42nd Annual Australasian Conference on Combinatorial Mathematics and Combinatorial Computing, which was held at UNSW in December 2019.
  • I was on the Programme Committee of the 2020 annual Australian Mathematical Society meeting.

Professional affiliations and service positions

  • I am an Editor-in-Chief of the Electronic Journal of Combinatorics.
  • I am the Chair of the Women in Mathematics Special Interest Group (WIMSIG) of the Australian Mathematical Society (2021 - 2022).
  • I am a member of the Council of the Combinatorial Mathematics Society of Australasia (CMSA).
  • I am on the Executive Committee and the Equity, Diversity and Inclusion Committee of the School of Mathematics and Statistics.

My Research Supervision

  • Haya Aldosari, PhD student: asymptotic enumeration of hypergraphs with given degrees and forbidden edges
  • James Ross, Masters student: sampling algorithms for regular hypergraphs
  • Rutvik Oza, Masters student: Cops and Robbers game on directed graphs

My Teaching

I teach a range of courses within the School of Mathematics and Statistics, from first year courses such as MATH1081 Discrete Mathematics to the Honours course MATH5425 Graph Theory.

I also developed an online Professional Development course for high school teachers (hosted by OpenLearning), covering the new Networks and Paths syllabus. I regularly take part in the School's Teacher's Professional Development workshops, delivering this material to teachers face-to-face.