## 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
A note on the matching numbers of triangle-free graphs
β Scribed by Roberto W. Frucht; Reinaldo E. Giudici
- Publisher
- John Wiley and Sons
- Year
- 1985
- Tongue
- English
- Weight
- 137 KB
- Volume
- 9
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
## Abstract Lower bounds on the size of a maximum bipartite subgraph of a triangleβfree __r__βregular graph are presented.
## Abstract The distance coloring number __X__~__d__~(__G__) of a graph __G__ is the minimum number __n__ such that every vertex of __G__ can be assigned a natural number __m__ β€ __n__ and no two vertices at distance __i__ are both assigned __i__. It is proved that for any natural number __n__ ther
If a graph has q 2 +q+1 vertices (q>13), e edges and no 4-cycles then e 1 2 q(q+1) 2 . Equality holds for graphs obtained from finite projective planes with polarities. This partly answers a question of Erdo s from the 1930's. 1996 Academic Press, Inc. ## 1. Results Let f (n) denote the maximum n