Mark Ellingham's Publications

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Submitted

• M. N. Ellingham and Justin Z. Schroeder, Orientable hamilton cycle embeddings of complete tripartite graphs I: latin square constructions. PDF preprint.
• M. N. Ellingham and Justin Z. Schroeder, Orientable hamilton cycle embeddings of complete tripartite graphs II: voltage graph constructions and applications. PDF preprint.

Published

• M. N. Ellingham, Michael D. Plummer and Gexin Yu, Linkage for the diamond and the path with four vertices, J. Graph Theory 70 (2012) 241-261. doi:10.1002/jgt.20612, PDF preprint.
• M. N. Ellingham and Justin Z. Schroeder, Nonorientable hamilton cycle embeddings of complete tripartite graphs, Discrete Mathematics 312 (2012) 1911-1917. doi:10.1016/j.disc.2012.02.012, PDF preprint.
• M. N. Ellingham and Justin Z. Schroeder, Distinguishing partitions and uniform asymmetric hypergraphs, Ars Mathematica Contemporanea 4 (2011) 111-123. amc.imfm.si/index.php/amc/article/view/195, PDF preprint.
• M. N. Ellingham and Xiaoya Zha, Orientable embeddings and orientable cycle double covers of projective-planar graphs, European J. Combinatorics 32 (2011) 495-509. doi:10.1016/j.ejc.2011.01.001, arxiv:0911.2713, PDF preprint.
• M. N. Ellingham and D. Christopher Stephens, The orientable genus of some joins of complete graphs with large edgeless graphs, Discrete Math. 309 (2009) 1190-1198. doi:10.1016/j.disc.2007.12.098, PDF preprint.
• M. N. Ellingham and Adam Weaver, Constructing all minimum genus embeddings of K_{3,n}, Electronic Notes in Discrete Math. 31 (2008) 293-298. (Extended abstract for conference.) doi:10.1016/j.endm.2008.06.059.
• Daniel P. Biebighauser and M. N. Ellingham, Prism-hamiltonicity of triangulations, J. Graph Theory 57 (2008) 181-197. doi:10.1002/jgt.20276, PDF preprint.
• M. N. Ellingham and D. Christopher Stephens, The nonorientable genus of joins of complete graphs with large edgeless graphs, J. Combinatorial Theory Series B 97 (2007) 827-845. doi:10.1016/j.jctb.2007.02.001, PDF preprint.
• M. N. Ellingham and Ken-ichi Kawarabayashi, 2-connected spanning subgraphs with low maximum degree in locally planar graphs, J. Combinatorial Theory Series B 97 (2007) 401-412. doi:10.1016/j.jctb.2006.07.002, PDF preprint.
• M. N. Ellingham, Chris Stephens and Xiaoya Zha, The nonorientable genus of complete tripartite graphs, J. Combinatorial Theory Series B 96 (2006) 529-559. doi:10.1016/j.jctb.2005.10.004, PDF preprint.
• M. N. Ellingham and Chris Stephens, Triangular embeddings of complete graphs (neighborly maps) with 12 and 13 vertices, J. Combinatorial Designs 13 (2005) 336-344. doi:10.1002/jcd.20048, PDF preprint.
• M. N. Ellingham, Chris Stephens and Xiaoya Zha, Counterexamples to the nonorientable genus conjecture for complete tripartite graphs, European J. Combinatorics 26 (2005) 387-399. doi:10.1016/j.ejc.2004.01.009.
• Mark N. Ellingham, Herbert Fleischner, Martin Kochol and Emanuel Wenger, Colorability of planar graphs with isolated nontriangular faces, Graphs and Combinatorics 20 (2004) 443-446. doi:10.1007/s00373-004-0574-z.
• M. N. Ellingham, Xiaoya Zha and Yi Zhang, Spanning 2-trails from degree sum conditions, J. Graph Theory 45 (2004) 298-319. doi:10.1002/jgt.10162, PDF preprint.
• Rommel Barbosa and M. N. Ellingham, A characterisation of cubic parity graphs, Australasian J. Combinatorics 28 (2003) 273-293. PDF preprint, PDF long version with full details (2 Apr. 2003).
• M. N. Ellingham and Xiaoya Zha, Separating cycles in doubly toroidal embeddings, Graphs and Combinatorics 19 (2003) 161-175. doi:10.1007/s00373-002-0491-y, PDF preprint.
• M. N. Ellingham, Yunsun Nam and H.-J. Voss, Connected (g,f)-factors, J. Graph Theory 39 (2002) 62-75. doi:10.1002/jgt.10019.
• M. N. Ellingham and D. Kirk Menser, Girth, minimum degree and circumference, J. Graph Theory 34 (2000) 221-233. doi:10.1002/1097-0118(200007)34:3<221::AID-JGT3>3.0.CO;2-T.
• M. N. Ellingham and Xiaoya Zha, Toughness, trees and walks, J. Graph Theory 33 (2000) 125-137. doi:10.1002/(SICI)1097-0118(200003)33:3<125::AID-JGT1>3.0.CO;2-X.
• M. N. Ellingham and Xiaoya Zha, The spectral radius of graphs on surfaces, J. Combinatorial Theory Series B 78 (2000) 45-56. doi:10.1006/jctb.1999.1926.
• Y. Caro, M. N. Ellingham and J. E. Ramey, Local structure when all maximal independent sets have equal weight, SIAM J. Discrete Math. 11 (1998) 644-654. doi:10.1137/S0895480196300479
• L. Clark, M. N. Ellingham and D. K. Menser, On the circumference of class 2 graphs, Utilitas Mathematica 53 (1998) 243-253.
• R. E. L. Aldred, M. N. Ellingham, R. L. Hemminger and P. Jipsen, P_3-isomorphisms for graphs, J. Graph Theory 26 (1997) 35-51. doi:10.1002/(SICI)1097-0118(199709)26:1<35::AID-JGT5>3.0.CO;2-I
• R. E. L. Aldred, M. N. Ellingham, R. L. Hemminger and D. A. Holton, Cycles in quasi-4-connected graphs, Australasian J. Combinatorics 15 (1997), 37-46.
• M. N. Ellingham and Luis Goddyn, List edge colourings of some 1-factorable multigraphs, Combinatorica 16 (1996) 343-352. doi:10.1007/BF01261320
• M. N. Ellingham, Spanning paths, cycles, trees and walks for graphs on surfaces, Proceedings of the Special Session in Graph Theory at the Amer. Math. Soc. conference, San Francisco, January 1995, Congressus Numerantium 115 (1996) 55-90.
• M. N. Ellingham, Vertex-switching reconstruction and folded cubes, J. Combinatorial Theory Series B 66 (1996) 361-364. doi:10.1006/jctb.1996.0027
• Richard Brunet, Mark N. Ellingham, Zhicheng Gao, Alice Metzlar and R. Bruce Richter, Spanning planar subgraphs of graphs in the torus and Klein bottle, J. Combinatorial Theory Series B 65 (1995) 7-22. doi:10.1006/jctb.1995.1041
• M. N. Ellingham, R. L. Hemminger and Kathryn E. Johnson, Contractible edges in longest cycles in nonhamiltonian graphs, Discrete Math. 133 (1994) 89-98. doi:10.1016/0012-365X(94)90018-3
• M. N. Ellingham and Zhicheng Gao, Spanning trees in locally planar triangulations, J. Combinatorial Theory Series B 61 (1994) 178-198. doi:10.1006/jctb.1994.1043
• M. N. Ellingham, Basic subgraphs and graph spectra, Australasian J. Combinatorics 8 (1993) 247-265.
• M. N. Ellingham, Sum graphs from trees, Ars Combinatoria 35 (1993) 335-349.
• S. R. Campbell, M. N. Ellingham and Gordon F. Royle, A characterisation of well-covered cubic graphs, J. Combinatorial Math. and Combinatorial Computing 13 (1993) 193-212.
• M. N. Ellingham and Gordon F. Royle, Vertex-switching reconstruction of subgraph numbers and triangle-free graphs, J. Combinatorial Theory Series B 54 (1992) 167-177. doi:10.1016/0095-8956(92)90048-3
• M. N. Ellingham, Vertex-switching, isomorphism and pseudosimilarity, J. Graph Theory 15 (1991) 563-572. doi:10.1002/jgt.3190150602
• M. N. Ellingham, L. Pyber and Xingxing Yu, Claw-free graphs are edge reconstructible, J. Graph Theory 12 (1988) 445-451. doi:10.1002/jgt.3190120317
• M. N. Ellingham, Recent progress in edge reconstruction, Proc. 17th Manitoba Conf. on Numerical Math. and Computing, Winnipeg, 1987, Congressus Numerantium 62 (1988) 3-20.
• M. N. Ellingham, Isomorphic factorization of regular graphs of even degree, J. Australian Math. Soc. (Series A) 44 (1988) 402-420.
• M. N. Ellingham, Isomorphic factorization of r-regular graphs into r parts, Discrete Math. 69 (1988) 19-34. doi:10.1016/0012-365X(88)90174-4
• M. N. Ellingham and N. C. Wormald, Isomorphic factorization of regular graphs and 3-regular multigraphs, J. London Math. Soc. (2) 37 (1988) 14-24. doi:10.1112/jlms/s2-37.121.14
• Wendy Myrvold, M. N. Ellingham and D. G. Hoffman, Bidegreed graphs are edge reconstructible, J. Graph Theory 11 (1987) 281-302. doi:10.1002/jgt.3190110304
• M. N. Ellingham and Y. Caro, Uniqueness of impartial edge-colourings, Ars Combinatoria 22 (1986) 59-71.
• I. Krasikov, M. N. Ellingham and Wendy Myrvold, Legitimate number decks for trees, Ars Combinatoria 21 (1986) 15-17.
• M. N. Ellingham, Petersen subdivisions in some regular graphs, Proc. 15th Southeastern Conf. on Combinatorics, Graph Theory and Computing, Baton Rouge, 1984, Congressus Numerantium 44 (1984) 33-40.
• M. N. Ellingham, D. A. Holton and C. H. C. Little, Cycles through ten vertices in 3-connected cubic graphs, Combinatorica 4 (1984) 265-273. doi:10.1007/BF02579136
• M. N. Ellingham and J. D. Horton, Non-hamiltonian 3-connected cubic bipartite graphs, J. Combinatorial Theory Series B 34 (1983) 350-353. doi:10.1016/0095-8956(83)90046-1
• M. N. Ellingham, The asymptotic connectivity of labelled coloured regular bipartite graphs, Combinatorics X, Proc. 10th Australian Conf. on Combinatorial Mathematics, Adelaide, 1982, Lecture Notes in Math. 1036, Springer, Berlin, 1983, 177-188.
• M. N. Ellingham, Constructing certain cubic graphs, Combinatorics IX, Proc. 9th Australian Conf. on Combinatorial Mathematics, Brisbane, 1981, Lecture Notes in Math. 952, Springer, Berlin, 1982, 252-274.

Theses

• M. N. Ellingham, Isomorphic Factorizations of Regular Graphs, thesis for Doctor of Philosophy, University of Waterloo, 1986.
• M. N. Ellingham, Cycles in 3-connected Cubic Graphs, thesis for Master of Science, University of Melbourne, 1982.