List-Edge Coloring Planar Graphs with Bounded Maximum Degree

Abstract

In this thesis we prove that triangulations of maximum degree 5 are 6-list-edge-colorable. We also find necessary conditions for maximum degree to extend a list-edge-precoloring to E(G) for a planar graph G. The techniques used for these two results are the kernel method, the quantitative combinatorial nullstellensatz, and the discharging method.