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Length of Longest Cycles in a Graph Whose Relative Length is at Least Two

✍ Scribed by Kenta Ozeki, Tomoki Yamashita

Book ID
118783099
Publisher
Springer Japan
Year
2011
Tongue
English
Weight
249 KB
Volume
28
Category
Article
ISSN
0911-0119

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πŸ“œ SIMILAR VOLUMES

Relative length of longest paths and cyc
Relative length of longest paths and cycles in 3-connected graphs
✍ Rao Li; Akira Saito; R.H. Schelp πŸ“‚ Article πŸ“… 2001 πŸ› John Wiley and Sons 🌐 English βš– 184 KB πŸ‘ 2 views

## 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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Several problems concerning the distribution of cycle lengths in a graph have been proposed by P. ErdΓΆs and colleagues. In this note two variations of the following such question are answered. In a simple graph where every vertex has degree at least three, must there exist two cycles whose lengths d