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On long cycles in a 2-connected bipartite graph

โœ Scribed by Hong Wang


Publisher
Springer Japan
Year
1996
Tongue
English
Weight
822 KB
Volume
12
Category
Article
ISSN
0911-0119

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๐Ÿ“œ SIMILAR VOLUMES


Long cycles in bipartite graphs
โœ Bill Jackson ๐Ÿ“‚ Article ๐Ÿ“… 1985 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 735 KB
Long Cycles in 3-Connected Graphs
โœ Guantao Chen; Xingxing Yu ๐Ÿ“‚ Article ๐Ÿ“… 2002 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 249 KB

Moon and Moser in 1963 conjectured that if G is a 3-connected planar graph on n vertices, then G contains a cycle of length at least Oรฐn log 3 2 รž: In this paper, this conjecture is proved. In addition, the same result is proved for 3-connected graphs embeddable in the projective plane, or the torus

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โœ Wang, Hong ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 244 KB ๐Ÿ‘ 2 views

It was conjectured in [Wang, to appear in The Australasian Journal of Combinatorics] that, for each integer k โ‰ฅ 2, there exists . This conjecture is also verified for k = 2, 3 in [Wang, to appear; Wang, manuscript]. In this article, we prove this conjecture to be true if n โ‰ฅ 3k, i.e., M (k) โ‰ค 3k. W