- Series
- Graph Theory Seminar
- Time
- Tuesday, December 7, 2021 - 3:45pm for 1 hour (actually 50 minutes)
- Location
- Skiles 005
- Speaker
- Guangming Jing – Augusta University – GJING@augusta.edu – https://www.augusta.edu/faculty/directory/view.php?id=GJING
- Organizer
- Anton Bernshteyn

Given a multigraph $G=(V,E)$, the *chromatic index* $\chi'(G)$ is the minimum number of colors needed to color the edges of $G$ such that no two incident edges receive the same color. Let $\Delta(G)$ be the maximum degree of $G$ and letÂ $\Gamma(G):=\max \big\{\frac{2|E(U)|}{|U|-1}:\,\, U \subseteq V, \,\, |U|\ge 3 \hskip 2mm

{\rm and \hskip 2mm odd} \big\}$. $\Gamma(G)$ is called the *density* of $G$. Clearly, the density is a lower bound for the chromatic index $\chi'(G)$. Moreover, this value can be computed in polynomial time. Goldberg and Seymour in the 1970s conjectured that $\chi'(G)=\lceil\Gamma(G)\rceil$ for any multigraph $G$ with $\chi'(G)\geq\Delta(G)+2$, known as the Goldberg-Seymour conjecture. In this talk we will discuss this conjecture and some related open problems. This is joint work with Guantao Chen and Wenan Zang.