Date and Time: 11/08/2024, 2 - 3 p.m.

Location: 25 Park Place, Room 1441

Colloquium: Overfull Conjecture and Multigraph Overfull Conjecture

Speaker: Dr. Songling Shan, Department of Mathematics and Statistics, Auburn University

Speaker's website: https://www.auburn.edu/cosam/faculty/math_stats/shan/index.htm

Title: Overfull Conjecture and Multigraph Overfull Conjecture

Abstract: Let $G$ be a (multi)graph with maximum degree denoted as $\Delta(G)$. An overfull subgraph $H$ of $G$ is a subgraph satisfying the condition $|E(H)| > \Delta(G)\left\lfloor\frac{1}{2}|V(H)|\right\rfloor$. In 1986, Chetwynd and Hilton proposed the Overfull Conjecture, stating that a simple graph $G$ with maximum degree $\Delta(G) > \frac{1}{3}|V(G)|$ has the chromatic index equal to $\Delta(G)$ if and only if it does not contain any overfull subgraphs. The multigraph version of the Overfull Conjecture was first formed by Stiebitz et al. in 2012, and it states the following:
\begin{quote}
Let $G$ be a multigraph such that $\Delta(G) > \frac{1}{3}r|V(G)|$, where $r$ is the maximum number of edges joining two vertices in $G$. Then the chromatic index of $G$ is equal to $\Delta(G)$ if and only if $G$ contains no $\Delta(G)$-overfull subgraph.
\end{quote}
In this talk, we will discuss some recent progress on both conjectures.

Speaker's biography: Songling Shan, a 2015 graduate of Georgia State University, is currently an Assistant Professor in the Department of Mathematics and Statistics at Auburn University. Prior to her current role, she held positions at Illinois State University (2018-2023) and Vanderbilt University (2015-2018). Her research interests are centered around Graph Theory and Combinatorics, particularly focusing on structural graph theory and graph edge colorings. Shan has authored over 40 papers, primarily published in renowned journals such as the Journal of Graph Theory and the Journal of Combinatorial Theory, Series B.

Host: Mark Grinshpon (mgrinshpon@gsu.edu)