Quickly proving the Andr\'asfai-Erd\H{o}s-S\'os-Theorem

Christian Reiher

Quickly proving the Andr\'asfai-Erd\H{o}s-S\'os-Theorem

Combinatorics 2016-03-22 v2

Authors: Christian Reiher

Abstract

Given an integer $r\gs 2$ , an important theorem first proved by B. Andr\'asfai, P. Erd\H{o}s, and V. T. S\'os states that any $K_{r+1}$ --free graph on $n$ vertices whose minimum degree is greater than $(3r-4)n/(3r-1)$ is $r$ --colourable, and determines the graphs that are extremal in this context. The purpose of this note is to give an alternative proof of this result using a different idea.

Keywords

Andrásfai-Erdős-Sós theorem extremal graph theory graph coloring minimum degree forbidden subgraphs alternative proof

Cite

@article{arxiv.1212.2521,
  title  = {Quickly proving the Andr\'asfai-Erd\H{o}s-S\'os-Theorem},
  author = {Christian Reiher},
  journal= {arXiv preprint arXiv:1212.2521},
  year   = {2016}
}

Comments

Withdrawn, since it turned out that the same proof was discovered earlier by Stephan Brandt, Combinatorica 23 (2003), no. 4, 693-696

Quickly proving the Andr\'asfai-Erd\H{o}s-S\'os-Theorem

Abstract

Keywords

Cite

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