The homomorphism threshold of $\{C_3, C_5\}$-free graphs

Shoham Letzter; Richard Snyder

The homomorphism threshold of $\{C_3, C_5\}$-free graphs

Combinatorics 2018-08-21 v3

Authors: Shoham Letzter , Richard Snyder

Abstract

We determine the structure of $\{C_3, C_5\}$ -free graphs with $n$ vertices and minimum degree larger than $n/5$ : such graphs are homomorphic to the graph obtained from a $(5k - 3)$ -cycle by adding all chords of length $1$ mod $5$ , for some $k$ . This answers a question of Messuti and Schacht. We deduce that the homomorphism threshold of $\{C_3, C_5\}$ -free graphs is $1/5$ , thus answering a question of Oberkampf and Schacht.

Keywords

homomorphism threshold {C3, C5}-free graphs minimum degree condition graph homomorphism extremal graph theory

Cite

@article{arxiv.1610.04932,
  title  = {The homomorphism threshold of $\{C_3, C_5\}$-free graphs},
  author = {Shoham Letzter and Richard Snyder},
  journal= {arXiv preprint arXiv:1610.04932},
  year   = {2018}
}

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30 pages, 13 figures

The homomorphism threshold of $\{C_3, C_5\}$-free graphs

Abstract

Keywords

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