# 1月18日 Seog-Jin Kim 教授学术报告（数学与统计学院）

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.

Seog-JinKim 教授毕业于美国伊利诺伊香槟分校（University of Illinois at Urbana-Champaign）,师从于Douglas Brent West,现为韩国建国大学（KonkukUniveristy）教授,主要研究领域是图的染色和图的结构,发表SCI 检索学术论文30余篇。

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