A Generalization of the Hsu-Robbins-Erdős Theorem
✍ Scribed by A. Spataru
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 306 KB
- Volume
- 187
- Category
- Article
- ISSN
- 0022-247X
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
## Abstract In this paper, we obtain an asymptotic generalization of Turán's theorem. We prove that if all the non‐trivial eigenvalues of a __d__‐regular graph __G__ on __n__ vertices are sufficiently small, then the largest __K__~__t__~‐free subgraph of __G__ contains approximately (__t__ − 2)/(__
For any integer r \ 1, let a(r) be the largest constant a \ 0 such that if E > 0 and 0 < c < c 0 for some small c 0 =c 0 (r, E) then every graph G of sufficiently large order n and at least edges contains a copy of any (r+1)-chromatic graph H of independence number a(H) [ (a -E) log n log(1/c) .