Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8903541 | European Journal of Combinatorics | 2018 | 12 Pages |
Abstract
The classical stability theorem of ErdÅs and Simonovits states that, for any fixed graph with chromatic number k+1â¥3, the following holds: every n-vertex graph that is H-free and has within o(n2) of the maximal possible number of edges can be made into the k-partite Turán graph by adding and deleting o(n2) edges. In this paper, we prove sharper quantitative results for graphs H with a critical edge, both for the ErdÅs-Simonovits Theorem (distance to the Turán graph) and for the closely related question of how close an H-free graph is to being k-partite. In many cases, these results are optimal to within a constant factor.
Related Topics
Physical Sciences and Engineering
Mathematics
Discrete Mathematics and Combinatorics
Authors
Alexander Roberts, Alex Scott,