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Small cycles and 2-factor passing through any given vertices in graphs

✍ Scribed by Jiuying Dong

Book ID
107619972
Publisher
Springer-Verlag
Year
2009
Tongue
English
Weight
300 KB
Volume
34
Category
Article
ISSN
1598-5865

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## Abstract In this article, we prove the following theorem. Let __k__ β‰₯ 3 be an integer, __G__ be a __k__‐connected graph with minimum degree __d__ and __X__ be a set of __k__ + 1 vertices on a cycle. Then __G__ has a cycle of length at least min {2d,|V(G)|} passing through __X__. This result give

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## Abstract A weighted graph is one in which every edge __e__ is assigned a nonnegative number, called the weight of __e__. The sum of the weights of the edges incident with a vertex Ο… is called the weighted degree of Ο…. The weight of a cycle is defined as the sum of the weights of its edges. In th