Finding Paths and Cycles of Superpolylogarithmic Length
β Scribed by Gabow, Harold N.
- Book ID
- 118181321
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 2007
- Tongue
- English
- Weight
- 288 KB
- Volume
- 36
- Category
- Article
- ISSN
- 0097-5397
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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 βconnected graph of order __n__ such that the minimum degree sum of four independent vertices is at least __n__+ 6
Let p(G) and c(G) be the order of a longest path and a longest cycle in a graph G, respectively. Let Ο 3 (G) = min{deg G x + deg G y + deg G z : {x, y, z} is an independent set of vertices of G}. Extending the result by Enomoto et al. (J Graph Th 20 (1995), 213-225) on the difference p(G) -c(G), we