报告题目：Packing edge colorings of subcubic graphs

报 告 人：刘旭钧，西交利物浦大学

报告时间：2024年6月27日（周四）下午15：00-16：00

报告地点：龙洞校区行政楼610

主 持 人：何伟骅

报告摘要：A matching (induced matching) is a set of edges $E$ such that each pair of edges in $E$ has distance at least two (three). A $(1^{\ell},2^k)$-packing edge-coloring of a graph $G$ is a partition of its edge set into $\ell$ matchings and $k$ induced matchings. Gastineau and Togni showed there are subcubic graphs that are not $(1,2,2,2,2,2,2)$-packing (abbreviated to $(1,2^6)$-packing) edge-colorable and not $(1^2,2^3)$-packing edge-colorable. They also asked the question “whether every subcubic graph is $(1,2^7)$-packing edge-colorable?”. Very recently, Hocquard, Lajou, and Lu\v zar showed that every subcubic graph is $(1,2^8)$-packing edge-colorable and $(1^2,2^5)$-packing edge-colorable. They also conjectured that every subcubic graph is $(1,2^7)$-packing edge-colorable. Furthermore, Gastineau and Togni, as well as Hocquard, Lajou, and Lu\v zar, have conjectured that every subcubic graph is $(1^2,2^4)$-packing edge-colorable.We confirm both conjectures. This is based on a joint work with Santana and Short, and a joint work with Gexin Yu.

专家简介：刘旭钧，西交利物浦大学助理教授。2020年8月博士毕业于美国伊利诺伊大学厄巴纳香槟分校，导师是Alexandr Kostochka教授。2020年8月至2021年8月在UIUC工程系做博士后，导师是 Olgica Milenkovic教授。 主要研究兴趣是图的染色，拉姆齐理论，和秘书问题。在 CPC, JGT，IEEE Transactions on Information Theory等组合数学与信息论期刊与会议共发表十余篇学术论文。