Article contents
A SUFFICIENT CONDITION FOR A PAIR OF SEQUENCES TO BE BIPARTITE GRAPHIC
Part of:
Graph theory
Published online by Cambridge University Press: 25 April 2016
Abstract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
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.
Keywords
MSC classification
Primary:
05C07: Vertex degrees
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 94 , Issue 2 , October 2016 , pp. 195 - 200
- Copyright
- © 2016 Australian Mathematical Publishing Association Inc.
References
Alon, N., Ben-Shimon, S. and Krivelevich, M., ‘A note on regular Ramsey graphs’, J. Graph Theory
64(3) (2010), 244–249.Google Scholar
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), 1494–1501.Google Scholar
Cairns, G. and Mendan, S., ‘Symmetric bipartite graphs and graphs with loops’, Discrete Math. Theor. Comput. Sci.
17(1) (2015), 97–102.Google Scholar
Cairns, G. and Mendan, S., ‘An improvement of a result of Zverovich–Zverovich’, Ars Math. Contemp.
10(1) (2016), 79–83.Google Scholar
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), 217–226.Google Scholar
Cairns, G., Mendan, S. and Nikolayevsky, Y., ‘A sharp refinement of a result of Zverovich–Zverovich’, Discrete Math.
338(7) (2015), 1085–1089.Google Scholar
Miller, J. W., ‘Reduced criteria for degree sequences’, Discrete Math.
313 (2013), 550–562.Google Scholar
Ryser, H. J., ‘Combinatorial properties of matrices of zeros and ones’, Canad. J. Math.
9 (1957), 371–377.Google Scholar
Zverovich, I. È. and Zverovich, V. È., ‘Contributions to the theory of graphic sequences’, Discrete Math.
105(1–3) (1992), 293–303.Google Scholar
- 2
- Cited by