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 \(K_v\).