Fisher, D.C. and J. Ryan, Bounds on the number of complete subgraphs, Discrete Mathematics 103 (1992) 313-320. Let G be a graph with a clique number w. For 1 s s w, let k, be the number of complete j subgraphs on j nodes. We show that k,,, c (j~l)(kj/(~))u""'. This is exact for complete balanced w-
Handle bases and bounds on the number of subgraphs
โ Scribed by John Donald; John Elwin; Richard Hager; Peter Salamon
- Publisher
- Elsevier Science
- Year
- 1987
- Tongue
- English
- Weight
- 788 KB
- Volume
- 42
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
Let \_(n, m, k) be the largest number \_ # [0, 1] such that any graph on n vertices with independence number at most m has a subgraph on k vertices with at lest \_ } ( k 2 ) edges. Up to a constant multiplicative factor, we determine \_(n, m, k) for all n, m, k. For log n m=k n, our result gives \_(
## Abstract Let __K__~1,__n__~ denote the star on __n__โ+โ1 vertices; that is, __K__~1,__n__~ is the complete bipartite graph having one vertex in the first vertex class of its bipartition and __n__ in the second. The special graph __K__~1,3~, called the __claw__, has received much attention in the