Universality for transversal Hamilton cycles

IF 0.8 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-01-10 DOI:10.1112/blms.13223

Candida Bowtell, Patrick Morris, Yanitsa Pehova, Katherine Staden

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引用次数: 0

Abstract

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