Strong Forms of Stability from Flag Algebra Calculations

Pikhurko, Oleg; Sliacan, Jakub; Tyros, Konstantinos

doi:10.48550/arxiv.1706.02612

Search citation statements

Order By: Relevance

Paper Sections

Select...

It Was Shown By Simonovits1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2018

Publication Types

Select...

Article1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Related results can be found in papers by Norin and Yepremyan [13,17], and Pikhurko, Sliacan and Tyros [14]. Finally, we note that results from this paper are applied in a joint paper with Natasha Morrison [11].…”

Section: It Was Shown By Simonovitssupporting

confidence: 73%

Stability results for graphs with a critical edge

Roberts

Scott

2018

European Journal of Combinatorics

View full text Add to dashboard Cite

The classical stability theorem of Erdős and Simonovits states that, for any fixed graph with chromatic number k + 1 ≥ 3, the following holds: every n-vertex graph that is H-free and has within o(n 2 ) of the maximal possible number of edges can be made into the k-partite Turán graph by adding and deleting o(n 2 ) edges. In this paper, we prove sharper quantitative results for graphs H with a critical edge, both for the Erdős-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.

show abstract

Section: It Was Shown By Simonovitssupporting

confidence: 73%