DMS Graduate Student Seminar

Speaker: Stacie Baumann

Title: Equitable $(s,p)$-edge-colorings of $K_v$

Abstract: This talk will focus on (not necessarily proper) $s$-edge-colorings of the complete graph, $K_v$, in which, for each vertex the edges incident with the vertex are colored using exactly $p$ colors.

In the spirit of proper edge-colorings, such $(s,p)$-edge-colorings are required to be equitable: the edges at each vertex are shared evenly among $p$ colors. Results obtained about the structure of these colorings will be discussed. The motivation behind this work will also be addressed, including a scheduling problem and extension to equitable $(s,p)$-block-colorings of $C_4$-decompositions of $K_v-F$, where $F$ is a 1-factor of $K_v$.