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Maximum Number of Contractible Edges on Hamiltonian Cycles of a 3-Connected Graph

✍ Scribed by Kyo Fujita

Publisher: Springer Japan
Year: 2002
Tongue: English
Weight: 252 KB
Volume: 18
Category: Article
ISSN: 0911-0119
DOI: 10.1007/s003730200033

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## Abstract Let __G__ be a graph on __p__ vertices with __q__ edges and let __r__ = __q__ − __p__ = 1. We show that __G__ has at most ${15\over 16} 2^{r}$ cycles. We also show that if __G__ is planar, then __G__ has at most 2^__r__ − 1^ = __o__(2^__r__ − 1^) cycles. The planar result is best possib