Events
DMS Combinatorics Seminar |
Time: Oct 09, 2024 (02:00 PM) |
Location: 328 Parker Hall |
Details: Speaker: Songling Shan (Auburn University) Title: Total coloring graphs with large maximum degree
Abstract: We prove that for any graph G, the total chromatic number of G is at most Δ(G)+2⌈|V(G)|Δ(G)+1⌉. This saves one color in comparison with a result of Hind from 1992 In particular, our result says that if Δ(G)≥12|V(G)|, then G has a total colouring using at most Δ(G)+4 colors. When G is regular and has a sufficient number of vertices, we can actually save an additional two colors. Specifically, we prove that for any 0<ε<1, there exists n0∈N such that: if G is an r-regular graph on n≥n0 vertices with r≥12(1+ε)n, then χT(G)≤Δ(G)+2. This confirms the Total Coloring Conjecture for such graphs G. This is joint work with Aseem Dalal and Jessica McDonald. |