Select Publications

Books

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

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

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://dx.doi.org/10.4324/9781315885018

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

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, vol. 99, http://dx.doi.org/10.1016/j.ejc.2021.103421

Dyer M; Greenhill C; Kleer P; Ross J; Stougie L, 2021, 'Sampling hypergraphs with given degrees', Discrete Mathematics, vol. 344, http://dx.doi.org/10.1016/j.disc.2021.112566

Greenhill C; Isaev M; Makai T; McKay BD, 2021, 'Degree sequences of sufficiently dense random uniform hypergraphs', , http://arxiv.org/abs/2106.08100v1

Greenhill C; Isaev M; McKay BD, 2021, 'Subgraph counts for dense random graphs with specified degrees', Combinatorics Probability and Computing, vol. 30, pp. 460 - 497, http://dx.doi.org/10.1017/S0963548320000498

Gao P; Greenhill C, 2021, 'Mixing time of the switch Markov chain and stable degree sequences', Discrete Applied Mathematics, vol. 291, pp. 143 - 162, http://dx.doi.org/10.1016/j.dam.2020.12.004

Cooper C; Dyer M; Greenhill C, 2021, 'A Triangle Process on Regular Graphs', Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 12757 LNCS, pp. 310 - 323, http://dx.doi.org/10.1007/978-3-030-79987-8_22

Dyer M; Greenhill C; Müller H, 2021, 'Counting independent sets in graphs with bounded bipartite pathwidth', Random Structures and Algorithms, http://dx.doi.org/10.1002/rsa.21003

Ayre P; Coja-Oghlan A; Greenhill C, 2021, 'Lower Bounds on the Chromatic Number of Random Graphs', Combinatorica, http://dx.doi.org/10.1007/s00493-021-4236-z

Greenhill C; Isaev M; Liang G, 2021, 'Spanning trees in random regular uniform hypergraphs', Combinatorics Probability and Computing, http://dx.doi.org/10.1017/S0963548321000158

Aldosari HS; Greenhill C, 2021, 'The average number of spanning hypertrees in sparse uniform hypergraphs', Discrete Mathematics, vol. 344, http://dx.doi.org/10.1016/j.disc.2020.112192

Chen C; Greenhill C, 2021, 'Threshold functions for substructures in random subsets of finite vector spaces', JOURNAL OF COMBINATORICS, vol. 12, pp. 157 - 183, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000605448000006&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

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, vol. 142, pp. 307 - 373, http://dx.doi.org/10.1016/j.jctb.2019.11.001

Mann RL; Mathieson L; Greenhill C, 2020, 'On the Parameterised Complexity of Induced Multipartite Graph Parameters', , http://arxiv.org/abs/2004.09938v1

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, vol. 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

Ayre P; Coja-Oghlan A; Greenhill C, 2019, 'Hypergraph coloring up to condensation', Random Structures and Algorithms, vol. 54, pp. 615 - 652, http://dx.doi.org/10.1002/rsa.20824

Cooper C; Dyer M; Greenhill C, 2019, 'Triangle-creation processes on cubic graphs', , http://arxiv.org/abs/1905.04490v1

Aldosari HS; Greenhill C, 2019, 'Enumerating sparse uniform hypergraphs with given degree sequence and forbidden edges', European Journal of Combinatorics, vol. 77, pp. 68 - 77, http://dx.doi.org/10.1016/j.ejc.2018.11.002

Cooper C; Dyer M; Greenhill C; Handley A, 2019, 'The flip Markov chain for connected regular graphs', Discrete Applied Mathematics, vol. 254, pp. 56 - 79, http://dx.doi.org/10.1016/j.dam.2018.06.019

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), vol. 11789 LNCS, pp. 298 - 310, http://dx.doi.org/10.1007/978-3-030-30786-8_23

Ayre P; Greenhill C, 2019, 'Rigid colorings of hypergraphs and contiguity', SIAM Journal on Discrete Mathematics, vol. 33, pp. 1575 - 1606, http://dx.doi.org/10.1137/18M1207211

Gao P; Greenhill C, 2019, 'Uniform generation of spanning regular subgraphs of a dense graph', Electronic Journal of Combinatorics, vol. 26, http://dx.doi.org/10.37236/8251

Ayre P; Coja-Oghlan A; Greenhill C, 2018, 'Lower bounds on the chromatic number of random graphs', , http://arxiv.org/abs/1812.09691v4

Greenhill C; Sfragara M, 2018, 'The switch Markov chain for sampling irregular graphs and digraphs', Theoretical Computer Science, vol. 719, pp. 1 - 20, http://dx.doi.org/10.1016/j.tcs.2017.11.010

Bright D; Greenhill C; Britz T; Ritter A; Morselli C, 2017, 'Criminal network vulnerabilities and adaptations', Global Crime, vol. 18, pp. 424 - 441, http://dx.doi.org/10.1080/17440572.2017.1377614

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, vol. 63, pp. 6 - 25, http://dx.doi.org/10.1016/j.ejc.2017.02.003

Blinovsky V; Greenhill C, 2016, 'Asymptotic enumeration of sparse uniform linear hypergraphs with given degrees', ELECTRONIC JOURNAL OF COMBINATORICS, vol. 23, http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000385228300003&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=891bb5ab6ba270e68a29b250adbe88d1

Blinovsky V; Greenhill C, 2016, 'Asymptotic enumeration of sparse uniform hypergraphs with given degrees', European Journal of Combinatorics, vol. 51, pp. 287 - 296, http://dx.doi.org/10.1016/j.ejc.2015.06.004

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, vol. 16, pp. 219 - 237, http://dx.doi.org/10.1080/17440572.2015.1039164

Dyer M; Frieze A; Greenhill C, 2015, 'On the chromatic number of a random hypergraph', Journal of Combinatorial Theory. Series B, vol. 113, pp. 68 - 122, http://dx.doi.org/10.1016/j.jctb.2015.01.002

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, vol. 31, pp. 262 - 278, http://dx.doi.org/10.1177/1043986214553378

Dyer M; Greenhill C; Ullrich M, 2014, 'Structure and eigenvalues of heat-bath Markov chains', Linear Algebra and Its Applications, vol. 454, pp. 57 - 71, http://dx.doi.org/10.1016/j.laa.2014.04.018

Greenhill C; Kwan M; Wind D, 2014, 'On the number of spanning trees in random regular graphs', Electronic Journal of Combinatorics, vol. 21, http://dx.doi.org/10.37236/3752

Bordewich M; Greenhill C; Patel V, 2014, 'Mixing of the Glauber dynamics for the ferromagnetic Potts model', Random Structures & Algorithms, vol. 48, pp. n/a - n/a, http://dx.doi.org/10.1002/rsa.20569

Greenhill C; Mckay BD, 2013, 'Asymptotic enumeration of sparse multigraphs with given degrees', SIAM Journal on Discrete Mathematics, vol. 27, pp. 2064 - 2089, http://dx.doi.org/10.1137/130913419

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

Greenhill CS; McKay BD, 2012, 'Counting loopy graphs with given degrees', Linear Algebra and its Applications, vol. 436, pp. 901 - 926, http://dx.doi.org/10.1016/j.laa.2011.03.052

Greenhill CS, 2011, 'A polynomial bound on the mixing time of a Markov chain for sampling regular directed graphs', Electronic Journal of Combinatorics, vol. 18, pp. #234 (49pp)

Canfield ER; Gao Z; Greenhill CS; McKay BD; Robinson RW, 2010, 'Asymptotic enumeration of correlation-immune boolean functions', Cryptography and Communications, vol. 2, pp. 111 - 126, http://dx.doi.org/10.1007/s12095-010-0019-x

Greenhill CS; Janson S; Rucinski A, 2010, 'On the number of perfect matchings in random lifts', Combinatorics Probability and Computing, vol. 19, pp. 791 - 817, http://dx.doi.org/10.1017/S0963548309990654

Greenhill CS; McKay BD, 2009, 'Random dense bipartite graphs and directed graphs with specified degrees', Random Structures and Algorithms, vol. 35, pp. 222 - 249, http://dx.doi.org/10.1002/rsa.20273

Canfield E; Greenhill CS; McKay BD, 2008, 'Asymptoic enumeration of dense 0-1 matrices with specified line sums', Journal of Combinatorial Theory Series A, vol. 115, pp. 32 - 66, http://dx.doi.org/10.1016/j.jcta.2007.03.009

Greenhill CS; McKay BD, 2008, 'Asymptotic enumeration of sparse nonnegative integer matrices with specified row and column sums', Advances in Applied Mathematics, vol. 41, pp. 459 - 481, http://dx.doi.org/10.1016/j.aam.2008.01.002

Greenhill CS; Holt F; Wormald NC, 2008, 'Expansion properties of a random regular graph after random vertex deletions', European Journal of Combinatorics, vol. 29, pp. 1139 - 1150, http://dx.doi.org/10.1016/j.ejc.2007.06.021

Cavenagh N; Greenhill CS; Wanless IM, 2008, 'The cycle structure of two rows in a random Latin square', Random Structures and Algorithms, vol. 33, pp. 286 - 309, http://dx.doi.org/10.1002/rsa.20216

Cooper C; Dyer M; Greenhill CS, 2007, 'Sampling regular graphs and a peer-to-peer network', Combinatorics Probability and Computing, vol. 16, pp. 557 - 593, http://dx.doi.org/10.1017/S0963548306007978

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, vol. 113, pp. 291 - 324, http://dx.doi.org/10.1016/j.jcta.2005.03.005


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