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Some recent progress on acyclic choosability of planar graphs

报告题目:Some recent progress on acyclic choosability of planar graphs

报告人:陈敏,浙江师范大学教授

报告时间:202291219:00-20:00

报告地点:腾讯会议235-589-263

报告摘要:

Let $G=(V,E)$ be a graph. A proper vertex coloring of $G$ is acyclic if $G$ contains no bicolored cycle. Namely, every cycle of$G$ must be colored with at least three colors. $G$ is acyclically$L$-colorable if for a given list assignment $L=\{L(v): v\inV\}$, there exists a proper acyclic coloring $\pi$ of $G$ such that$\pi(v)\in L(v)$ for all $v\in V$. If $G$ is acyclically $L$-colorable for any list assignment with $|L(v)|\geq k$ for all $v\inV$, then $G$ is acyclically $k$-choosable.This concept was introduced by Gr\“{u}nbaum in 1973.It is known that for any two integers $i$ and $j$ such that $\{i, j\}\subset  \{5,6, 7, 8, 9\}\setminus \{8,9\}$,every planar graph without $\{4,i,j\}$-cyclesis acyclically 4-choosable.In this talk, we shall complete the last remaining case by proving that every planar graph without $\{4,8,9\}$-cycles is acyclically 4-choosable.

报告人简介:

陈敏,浙江师范大学教授,博士生导师,数学与计算机科学学院副院长,省高校中青年学科带头人,省高校领军人才培养计划高层次拔尖人才,中国运筹学会图论组合分会理事、副秘书长,金华市女科技工作者协会秘书长。主要研究方向为图的染色理论。迄今在J. Combin. Theory Ser. BEuropean J. Combin.J. Graph TheoryDiscrete Math.Discrete Appl. Math. 以及中国科学等国内外学术刊物上发表60余篇SCI期刊学术论文。主持国家自然科学基金面上项目2项,主持国家自然科学基金青年基金1项,主持浙江省自然科学基金项目2项,主持留学回国人员科研启动基金1项,现为JOCO期刊的编委。成果先后获省自然科学学术奖一等奖、省科学技术奖二等奖、省首批担当作为好支书、省教育系统事业家庭兼顾型先进个人、省最美家庭


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