Maximising the Number of Cycles in Graphs with Forbidden Subgraphs

Natasha Morrison; Alexander Roberts; Alex Scott

Maximising the Number of Cycles in Graphs with Forbidden Subgraphs

Combinatorics 2020-03-20 v2

Authors: Natasha Morrison , Alexander Roberts , Alex Scott

Abstract

Fix $k \ge 2$ and let $H$ be a graph with $\chi(H) = k+1$ containing a critical edge. We show that for sufficiently large $n$ , the unique $n$ -vertex $H$ -free graph containing the maximum number of cycles is $T_k(n)$ . This resolves both a question and a conjecture of Arman, Gunderson and Tsaturian.

Keywords

graph cycles forbidden subgraphs chromatic number critical edge extremal graph theory

Cite

@article{arxiv.1902.08133,
  title  = {Maximising the Number of Cycles in Graphs with Forbidden Subgraphs},
  author = {Natasha Morrison and Alexander Roberts and Alex Scott},
  journal= {arXiv preprint arXiv:1902.08133},
  year   = {2020}
}

Comments

36 pages

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