Topic:Signed coloring of $k$-chromatic graphs
Speaker: Professor Seog-Jin Kim
Event date: 1/18/2019
Event time: 9:00 a.m.
Venue: Lecture Hall 1508, Building 9
Sponsor: School of Mathematics and Statistics, Institute of Science and Technology
Abstract: Asigned graph is a pair (G, \sigma), where G is a graph and $\sigma$ is a signature of G which assigns to each edge e a sign $\sigma(e) \in {1, -1}$. A k-coloringof G is a mapping $f: V(G) \to N_k$ such that for each edge e=uv, $f(x) \ne\sigma(e) f(y)$, where $N_k = \{\pm 1, \pm 2, …, \pm q\}$ if k=2q is even and $N_k= \{0, \pm 1, \pm 2, …, \pm q\}$ if k=2q+1 is odd. The chromatic number$\chi_{\pm}(G, \sigma)$ of (G, \sigma)is the minimum k such that $(G, \sigma)$ has a k-coloring. We define the signed chromatic number of a graph G to be $\chi_{\pm}(G) = max \{ \chi_{\pm}(G,\sigma): \sigma \mbox{ is a signature ofG} \}$. In this talk, we will give an overview of signed coloring, and present recent results in signed coloring. This is joint work with Ringi Kim and Xuding Zhu.