报告题目：Majority coloring of digraphs

报 告 人：蔡建生，潍坊学院 教授

报告摘要：A majority $k$-coloring of a digraph $D$ with $k$ colors is an assignment $c:V(D) \rightarrow \{1,2,\cdots ,k\}$, such that for every $v\in V(D)$, we have $c(w)=c(v)$ for at most half of all out-neighbors $w\in N^+(v)$. Kreutzer et al. conjectured that every digraph admits a majority 3-coloring. For a natural number $k\geq 2$, a $\frac{1}{k}$-majority coloring of a digraph is a coloring of the vertices such that each vertex receives the same color as at most a $\frac{1}{k}$ proportion of its out-neighbours. Gir$\widetilde{a}$o et al. conjectured that every digraph admits a $\frac{1}{k}$-majority $(2k-1)$-coloring. In this paper, we prove that Kreutzer's conjecture is true for digraphs under some conditions, which improves Kreutzer's results. Moreover, we discuss the majority 3-coloring of random digraph with some conditions.

报告人简介：蔡建生，潍坊学院数学与信息科学学院教授、理学博士、中国工业与应用数学学会图论组合及其应用专业委员会常务委员、中国工业与应用数学学会信息和通讯领域的数学专业委员会委员、山东省数学会高等数学专业委员会常务理事、潍坊市五一劳动奖章获得者。长期从事图论和组合数学的研究，发表本专业学术论文80余篇，主持国家自然科学基金面上项目两项，参与国家自然科学基金项目和山东省自然科学基金项目多项。获得山东省自然科学三等奖一项，获得山东省高等学校优秀科研成果奖多项。

报告时间：2023年3月2日14:00-16:00

报告地点：文渊楼B座b208

主办单位：伟德国际1946源自英国