Universality for transversal Hamilton cycles

Bowtell, Candy; Morris, Patrick; Pehova, Yanitsa and Staden, Katherine (2024). Universality for transversal Hamilton cycles. Bulletin of the London Mathematical Society (In press).

DOI: https://doi.org/10.48550/arXiv.2310.04138

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 $G_{\chi(i)}$.

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