报告地点：腾讯会议号 421-277-923
报告人简介：陈敏，浙江师范大学教授，博士生导师，教务处副处长，曾任数计学院副院长。省高校中青年学科带头人，省高校高层次拔尖人才，中国运筹学会图论组合分会理事、副秘书长，第九届世界华人数学家大会（ICCM 2022）45分钟特邀报告人。主要研究方向为图的染色理论。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。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。
报告摘要：Let $G=(V, E)$ be a graph.If the vertex set $V(G)$ can be partitioned into two non-empty subsets $V_1$ and $V_2$ such that $G[V_1]$ and $G[V_2]$ are forests with maximum degree at most $d_1$ and $d_2$, then we say that $G$ has a $(F_{d_1},F_{d_2})$-partition. In this talk, we prove that every graph $G$ with mad$(G)\le\frac{16}{5}$ admits an $(F_{1}, F_{4})$-partition. As a corollary, every planar graph with girth at least $6$ admits an $(F_{1}, F_{4})$-partition. It improves a result in [O. V. Borodin, A. V. Kostochka, Defective $2$-colorings of sparse graphs,J. Combin. Theory Ser. B.]. This is joint work with Andr\'{e} Raspaud and Weiqiang Yu.