Weighted variants of the Andr\'asfai-Erd\H{o}s-S\'os Theorem

Clara M. Lüders; Christian Reiher

Weighted variants of the Andr\'asfai-Erd\H{o}s-S\'os Theorem

Combinatorics 2020-12-18 v2

Authors: Clara M. Lüders , Christian Reiher

Abstract

A well known result due to Andr\'asfai, Erd\H{o}s, and S\'os asserts that for $r\ge 2$ every $K_{r+1}$ -free graph on $n$ vertices with $\delta(G)>\frac{3r-4}{3r-1}n$ is $r$ -partite. We study related questions in the context of weighted graphs, which are motivated by recent work on the Ramsey-Tur\'an problem for cliques.

Keywords

weighted graphs andrásfai-erdős-sós theorem k-free graphs r-partite ramsey-turán problem minimum degree

Cite

@article{arxiv.1710.09652,
  title  = {Weighted variants of the Andr\'asfai-Erd\H{o}s-S\'os Theorem},
  author = {Clara M. Lüders and Christian Reiher},
  journal= {arXiv preprint arXiv:1710.09652},
  year   = {2020}
}

Comments

8 figures; revised according to referee report

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