报告题目： Anti-Ramsey number of edge-disjoint rainbow spanning trees

报告人：王智宇， 路易斯安那州立大学

地点：管理科研楼1318

时间：7月4号下午4：00-5：00

摘要：An edge-colored graph $H$ is called \textit{rainbow} if every edge of $H$ receives a different color. Given any host multigraph $G$, the \textit{anti-Ramsey} number of $t$ edge-disjoint rainbow spanning trees in $G$, denoted by $r(G,t)$, is defined as the maximum number of colors in an edge-coloring of $G$ containing no $t$ edge-disjoint rainbow spanning trees. For any vertex partition $P$, let $E(P,G)$ be the set of non-crossing edges in $G$ with respect to $P$. We determine $r(G,t)$ for all host multigraphs $G$: $r(G,t)=|E(G)|$ if there exists a partition $P_0$ with $|E(G)|-|E(P_0,G)|<t(|P_0|-1)$; and $r(G,t)=\max_{P\colon |P|\geq 3} \{|E(P,G)|+t(|P|-2)\}$ otherwise.