A note on the independence number of triangle-free graphs
β Scribed by James B. Shearer
- Publisher
- Elsevier Science
- Year
- 1983
- Tongue
- English
- Weight
- 188 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract We show that a maximal triangleβfree graph on __n__ vertices with minimum degree Ξ΄ contains an independent set of 3Ξ΄ β __n__ vertices which have identical neighborhoods. This yields a simple proof that if the binding number of a graph is at least 3/2 then it has a triangle. This was con
## Abstract Lower bounds on the size of a maximum bipartite subgraph of a triangleβfree __r__βregular graph are presented.
We show that a &-
Let (Y(G~,~) denote the independence number of the random graph Gn,p. Let d = np. We show that if E > 0 is fixed then with probability going to 1 as n + m cu(G& -$t (log d -log log dlog 2 + 1) < 7 provided d, s d = o(n), where d, is some fixed constant.
In this paper we use the degree sequence, order, size and vertex connectivity of a K 1,,+ 1 -free graph or of an almost claw-free graph to obtain several upper bounds on its independence number. We also discuss the sharpness of these results.