题目：An (F1, F4)-partition of planar graphs with girth 6
主讲人：陈敏
时间：2023-03-21 10:00-12:00
地点：16208会议室
举办部门：工学院数学系
讲座要点：Let G = (V, E) be a graph. If the vertex set V (G) can be partitioned into two non-empty subsets V1 and V2 such that G[V1] and G[V2] are graphs with maximum degree at most d1 and d2, respectively, then we say that G has a (∆d1 , ∆d2 )-partition. A similar definition can be given for the notation (Fd1 , Fd2 )-partition if G[Vi ] is a forest with maximum degree at most di , where i ∈ {1, 2}. The maximum average degree of G is defined to be mad(G) = max{ 2|E(H)| |V (H)| : H ⊆ G}. In this talk, we prove that every graph G with mad(G) ≤ 16 5 admits an (F1, F4)-partition. As a corollary, every planar graph with girth at least 6 admits an (F1, F4)-partition. This improves a result in [O. V. Borodin, A. V. Kostochka, Defective 2-colorings of sparse graphs, J. Combin. Theory Ser. B 104 (2014) 72–80.] saying that every graph G with mad(G) ≤ 16 5 admits a (∆1, ∆4)-partition. This is joint work with André Raspaud and Weiqiang Yu.
主讲人简介：陈敏，获法国波尔多第一大学和苏州大学双博士学位，现为浙江师大数学与计算机科学学院教授、博士生导师，浙师大教务处处长。曾获浙江省首批“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”，校“优秀共产党员”，连续三届获评校“我心目中的好老师”、六次获评校“优秀班主任”，入选第二批浙江省高校领军人才培养计划“高层次拔尖人才”，入选校首批学术名师培育计划，现为省高校中青年学科带头人，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. B、European J. Combin.、J. Graph Theory、Discrete 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3项，主持留学回国人员科研启动基金1项，主持浙江省重中之重开放项目1项，现为JOCO期刊的编委。
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