Georgia Institute of Technology College of Sciences

The Goldberg-Seymour Conjecture asserts that if the chromatic index $\chi'(G)$ of a loopless multigraph $G$ exceeds its maximum degree $\Delta(G) +1$, then it must be equal to another well known lower bound $\Gamma(G)$, defined as

$\Gamma(G) = \max\left\{\biggl\lceil  \frac{ 2|E(H)|}{(|V (H)|-1)}\biggr\rceil \ : \  H \subseteq G \mbox{ and } |V(H)| \mbox{ odd }\right\}.$

In this talk, we will outline a short proof,  obtained recently with  Hao, Yu, and Zang.