On long cycles in a 2-connected bipartite graph
โ 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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๐ SIMILAR VOLUMES
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 ร: 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
It was conjectured in [Wang, to appear in The Australasian Journal of Combinatorics] that, for each integer k โฅ 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 โฅ 3k, i.e., M (k) โค 3k. W