Relative length of longest paths and longest cycles in triangle-free graphs
β 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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π SIMILAR VOLUMES
## 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 3βconnected graph of order __n__ such that $\textstyle{\sum^{4}\_{i=1}\,{\rm deg}\_{G}\,x\_{i} \ge {3\over2}\,n + 1}$
## 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 βconnected graph of order __n__ such that the minimum degree sum of four independent vertices is at least __n__+ 6
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.