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A SUFFICIENT CONDITION FOR A PAIR OF SEQUENCES TO BE BIPARTITE GRAPHIC

  • GRANT CAIRNS (a1), STACEY MENDAN (a2) and YURI NIKOLAYEVSKY (a3)
Abstract

We present a sufficient condition for a pair of finite integer sequences to be degree sequences of a bipartite graph, based only on the lengths of the sequences and their largest and smallest elements.

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Corresponding author
Y.Nikolayevsky@latrobe.edu.au
References
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[1] Alon, N., Ben-Shimon, S. and Krivelevich, M., ‘A note on regular Ramsey graphs’, J. Graph Theory 64(3) (2010), 244249.
[2] Barrus, M. D., Hartke, S. G., Jao, K. F. and West, D. B., ‘Length thresholds for graphic lists given fixed largest and smallest entries and bounded gaps’, Discrete Math. 312(9) (2012), 14941501.
[3] Cairns, G. and Mendan, S., ‘Symmetric bipartite graphs and graphs with loops’, Discrete Math. Theor. Comput. Sci. 17(1) (2015), 97102.
[4] Cairns, G. and Mendan, S., ‘An improvement of a result of Zverovich–Zverovich’, Ars Math. Contemp. 10(1) (2016), 7983.
[5] Cairns, G., Mendan, S. and Nikolayevsky, Y., ‘A sharp refinement of a result of Alon, Ben-Shimon and Krivelevich on bipartite graph vertex sequences’, Australas. J. Combin. 60 (2014), 217226.
[6] Cairns, G., Mendan, S. and Nikolayevsky, Y., ‘A sharp refinement of a result of Zverovich–Zverovich’, Discrete Math. 338(7) (2015), 10851089.
[7] Gale, D., ‘A theorem on flows in networks’, Pacific J. Math. 7 (1957), 10731082.
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[10] Zverovich, I. È. and Zverovich, V. È., ‘Contributions to the theory of graphic sequences’, Discrete Math. 105(1–3) (1992), 293303.
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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