Skip to main content Accessibility help
×
Home

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.

Copyright

Corresponding author

References

Hide All
[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.
[8] Miller, J. W., ‘Reduced criteria for degree sequences’, Discrete Math. 313 (2013), 550562.
[9] Ryser, H. J., ‘Combinatorial properties of matrices of zeros and ones’, Canad. J. Math. 9 (1957), 371377.
[10] Zverovich, I. È. and Zverovich, V. È., ‘Contributions to the theory of graphic sequences’, Discrete Math. 105(1–3) (1992), 293303.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

Keywords

MSC classification

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed