应兰州大学数学与统计学院张和平教授和高毓平副教授邀请，英国伯明翰大学Allan Lo副教授将于2026年7月2日做线上学术报告。
报告题目：Compatible HamiltonCycles
报告时间：2026年7月2日17:00
Zoom ID：951 968 5396（密码：20260702）
报告摘要：The renowned theorem of Dirac states that if $G$ is a graph with minimum degree at least $n/2$ then $G$ has a Hamilton cycle. A natural generalisation asks what properties of an edge-colouring of $G$ guarantee the existence of a properly edge-coloured Hamilton cycle in $G$.
This concept can be further generalised as follows: an incompatibility system for $G$ is a set $\mathcal{F}$ of `forbidden' pairs of adjacent edges, that is, $\mathcal{F}\subseteq \{\{uv,vw\}\in \binom{E(G)}2\}$. A cycle in $G$ is then compatible if no two of its edges form a pair in $\mathcal{F}$. The system $\mathcal{F}$ is called $\mu n$-bounded if for all $v\in V(G)$ and $uv\in E(G)$, there are at most $\mu n$ pairs $\{uv,vw\} \in \mathcal{F}$. How small must $\mu$ be to guarantee the existence of a compatible Hamilton cycle in $G$?
Krivelevich, Lee and Sudakov showed that $\mu=10^{-16}$ suffices (for $n$ large), while an example of Bollob\'as and Erd\H{o}s shows that $\mu\leq 1/4$ is necessary. In this talk, we show that if $\delta (G) \ge (1/2+\varepsilon)n$, then we have $1/6 \le \mu \le 1/8$.
This is joint work with Natalie Behague (Dublin City), Francesco Di Braccio (LSE) and Bertille Granet (Warwick).
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报告人简介
Allan Lo，英国伯明翰大学（University of Birmingham）数学学院副教授，在剑桥大学（University of Cambridge）分别获得学士、硕士、博士学位，博士导师为Andrew Thomason教授。他的主要研究方向为组合数学、离散数学、极值图论、超图以及Ramsey理论等。在Memoirs of the American Mathematical Society、Advances in Mathematics、Proceedings of the London Mathematical Society、Journal of Combinatorial Theory Series A、Journal of Combinatorial Theory Series B、Combinatorica、Journal of Graph Theory、SIAM Journal on Discrete Mathematics、Combinatorics, Probability and Computing、Random Structures & Algorithms等国际著名期刊上发表学术论文五十余篇。他曾多次获得英国工程与自然科学研究理事会（EPSRC）项目资助。2021年，他与合作者共同获得由美国数学会（AMS）和数学优化学会（MOS）联合颁发的Delbert Ray Fulkerson Prize。
甘肃省计算数学基础学科研究中心
数学与统计学院
萃英学院
2026年6月29日
