Universality for transversal Hamilton cycles

Candida Bowtell; Patrick Morris; Yanitsa Pehova; Katherine Staden

Universality for transversal Hamilton cycles

Combinatorics 2023-10-09 v1

Authors: Candida Bowtell , Patrick Morris , Yanitsa Pehova , Katherine Staden

Abstract

Let $\mathbf{G}=\{G_1, \ldots, G_m\}$ be a graph collection on a common vertex set $V$ of size $n$ such that $\delta(G_i) \geq (1+o(1))n/2$ for every $i \in [m]$ . We show that $\mathbf{G}$ contains every Hamilton cycle pattern. That is, for every map $\chi: [n] \to [m]$ there is a Hamilton cycle whose $i$ -th edge lies in $G_{\chi(i)}$ .

Keywords

hamilton cycles graph cycles dynamical systems

Cite

@article{arxiv.2310.04138,
  title  = {Universality for transversal Hamilton cycles},
  author = {Candida Bowtell and Patrick Morris and Yanitsa Pehova and Katherine Staden},
  journal= {arXiv preprint arXiv:2310.04138},
  year   = {2023}
}

Comments

18 pages

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