DMS Combinatorics Seminar

Speaker: Owen Henderschedt (Auburn University)

Title: List-orientations and total-coloring extensions of planar graphs

In this talk, I will discuss two problems in graph theory. I will briefly consider the first, which concerns finding orientations that satisfy prescribed out-degree restrictions. The second focuses on coloring extensions, asking when a graph with some precolored subgraphs can be totally colored without introducing additional colors. Inspired by vertex- and edge-coloring extension problems, we initiate the study of total-coloring extensions, proposing several conjectures and proving them for planar graphs.

This is joint work with Jessica McDonald.