On the independence number in K1, r+1-free graphs
✍ Scribed by Zdeněk Ryjáček; Ingo Schiermeyer
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 353 KB
- Volume
- 138
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
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.
📜 SIMILAR VOLUMES
## Abstract In this paper, we investigate the Hamiltonicity of __K__~1,r~‐free graphs with some degree conditions. In particular, let __G__ be a __k__‐connected grph of order __n__≧3 which is __K__~1,4~‐free. If magnified image for every independent set {__v__~0~, __v__~1~, …, __v__~k~} then __G__
We show that if G is a K r -free graph on N, there is an independent set in G which contains an arbitrarily long arithmetic progression together with its difference. This is a common generalization of theorems of Schur, van der Waerden, and Ramsey. We also discuss various related questions regarding
## Abstract For integers __d__≥0, __s__≥0, a (__d, d__+__s__)‐__graph__ is a graph in which the degrees of all the vertices lie in the set {__d, d__+1, …, __d__+__s__}. For an integer __r__≥0, an (__r, r__+1)‐__factor__ of a graph __G__ is a spanning (__r, r__+1)‐subgraph of __G__. An (__r, r__+1)‐