| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 4651930 | Electronic Notes in Discrete Mathematics | 2015 | 8 Pages |
Abstract
We study the behaviour of Kr+1-free graphs G of almost extremal size, that is, typically, e(G)=ex(n,Kr+1)−O(n). We show that such graphs must have a large amount of symmetry. In particular, if G is saturated, then all but very few of its vertices must have twins. As a corollary, we obtain a new proof of a theorem of Simonovits on the structure of extremal graphs with ω(G)≤r and χ(G)≥k for fixed k≥r≥2.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
