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Relative length of longest paths and longest cycles in triangle-free graphs

✍ Scribed by Daniel Paulusma; Kiyoshi Yoshimoto


Book ID
108113804
Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
215 KB
Volume
308
Category
Article
ISSN
0012-365X

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πŸ“œ SIMILAR VOLUMES


Relative length of longest paths and cyc
✍ 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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## 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

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In this article w e show that the standard results concerning longest paths and cycles in graphs can be improved for K,,,-free graphs. We obtain as a consequence of these results conditions for the existence of a hamiltonian path and cycle in K,,,-free graphs.