115周年校庆“学术华农”系列活动之0182 数信学院学术报告:Rainbow cycles through specified vertices

报告时间:2024611日下午15:30

报告地点:数学与信息学院数学系715教室

报告题目:Rainbow cycles through specified vertices

报告摘要:An edge-coloured cycle is rainbow if the edges have distinct colours. Let $G$ be a graph such that any $k$ vertices lie in a cycle of $G$. The $k$-rainbow cycle index of $G$, denoted by $crx_k(G)$, is the minimum number of colours required to colour the edges of $G$ such that, for every set $S$ of $k$ vertices in $G$, there exists a rainbow cycle in $G$ containing $S$. In this paper, we will first prove some results about the parameter $crx_k(G)$ for general graphs $G$. One of the results is a classification of all graphs $G$ such that $crx_k(G)=e(G)$, for $k=1,2$. We will also determine $crx_k(G)$ for some specific graphs $G$, including wheels, complete graphs, complete bipartite and multipartite graphs, and discrete cubes.

个人简介:廖仲行(Henry Liu),中山大学副教授。2006年于美国孟菲斯大学取得博士学位,师从Bela Bollobas教授。20062017年,在长沙中南大学、葡萄牙里斯本斯大学、英国伦敦大学大学、西班牙加泰罗尼亚理工大学、匈牙利Alfred Renyi研究所从事博士后和研究员工作。20178月至今在中山大学工作。研究兴趣包括极值图论、染色问题、随机组合。大约有30篇学术论文发表在《SIAM Journal on Discrete Mathematics》、《European Journal of Combinatorics》、《Journal of Graph Theory》、《Discrete Mathematics》、《Discrete Applied Mathematics》、等杂志。