## Abstract For a vertex __v__ of a graph __G__, we denote by __d__(__v__) the __degree__ of __v__. The __local connectivity__ ฮบ(__u, v__) of two vertices __u__ and __v__ in a graph __G__ is the maximum number of internally disjoint __u__ โ__v__ paths in __G__, and the __connectivity__ of __G__ is
Local and Global Clique Numbers
โ Scribed by N. Linial; Y. Rabinovich
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 416 KB
- Volume
- 61
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
โฆ Synopsis
Consider a graph (G) with the property that any set of (p) vertices in (G) contains a (q)-clique. Fairly tight lower bounds are proved on the clique number of (G) as a function of (p, q) and the number of vertices in (G). 1994 Academic Press, Inc.
๐ SIMILAR VOLUMES
## Abstract The Hadwiger number ${h}({G})$ of a graph __G__ is the maximum integer __t__ such that ${K}\_{t}$ is a minor of __G__. Since $\chi({G})\cdot\alpha({G})\geq |{G}|$, Hadwiger's conjecture implies that ${h}({G})\cdot \alpha({G})\geq |{G}|$, where $\alpha({G})$ and $|{G}|$ denote the indepe
In this note we find the local and mean k-Ramsey numbers for many trees for which the Erdo s So s tree conjecture holds. ## 2000 Academic Press The usual Ramsey number R(G, k) is the smallest positive integer n such that any coloring of the edges of K n by at most k colors contains a monochromatic
## Abstract An Erratum has been published for this article in Journal of Graph Theory 48: 329โ330, 2005. Let __M__ be a set of positive integers. The distance graph generated by __M__, denoted by __G__(__Z, M__), has the set __Z__ of all integers as the vertex set, and edges __ij__ whenever |__i__