수학과

*초록: The strong edge coloring of a graph is a coloring of edges so that each color induces a matching, and the minimum number of colors needed for the strong edge coloring of a graph $G$ is called the strong chromatic index of $G$. Since a strong edge coloring is a stronger concept of an edge coloring which is one of the most important topics in graph theory, there are a lot of results and conjectures regarding the strong chromatic index. For instance, Erd\H{o}s and Ne\v{s}et\v{r}il in 1985 conjectured that every graph $G$ has strong chromatic index at most $\frac{5\Delta(G)^2}{4}$,  which is known as the strong edge coloring conjecture. Since the strong edge coloring conjecture is one of the  deepest conjectures in graph theory, many questions regarding the conjecture have been proposed. In this talk, we present recent results and variations of the strong edge coloring conjecture.