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Relative Length of Longest Paths and Cycles in 2-Connected Graphs

✍ Scribed by Fan, Genghua; Ji, Naidan

Book ID
118197032
Publisher
Society for Industrial and Applied Mathematics
Year
2009
Tongue
English
Weight
164 KB
Volume
23
Category
Article
ISSN
0895-4801

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## Abstract For a graph __G__, let __p(G)__ denote the order of a longest path in __G__ and __c(G)__ the order of a longest cycle in __G__, respectively. We show that if __G__ is a 3‐connected graph of order __n__ such that $\textstyle{\sum^{4}\_{i=1}\,{\rm deg}\_{G}\,x\_{i} \ge {3\over2}\,n + 1}$

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## Abstract For a graph __G__, __p__(__G__) and __c__(__G__) denote the order of a longest path and a longest cycle of __G__, respectively. In this paper, we prove that if __G__ is a 3 ‐connected graph of order __n__ such that the minimum degree sum of four independent vertices is at least __n__+ 6