DMS Combinatorics Seminar

Speaker: Yuping Gao (Lanzhou University) 

Title:Vertex-distinguishing edge coloring of graphs

Abstract: Given an integer \(k\ge1\), an edge-\(k\)-coloring of a graph \(G\) is an assignment of \(k\) colors \(1,\ldots,k\) to the edges of \(G\) such that no two adjacent edges receive the same color. A vertex-distinguishing edge-\(k\)-coloring of \(G\) is an edge-\(k\)-coloring  such that for any two distinct vertices \(u\) and \(v\), the set  of  colors taken  from all the edges incident with \(u\) is different from that taken from all the edges incident with \(v\). The vertex-distinguishing chromatic index, denoted \(\chi'_{vd}(G)\), is  the smallest value \(k\) such that \(G\) has  a vertex-distinguishing edge-\(k\)-coloring. In this talk, we present some recent progress on vertex-distinguishing edge colorings.

This work is joint with Songling Shan, Guanghui Wang, and Yiming Zhou.