报告人：胡小兰 副教授 华中师范大学

报告时间： 2021年4月21日，下午15：00-

腾讯会议ID: 409105463

摘要：A graph G is (a:b)-colorable if there exists an assignment of b-element subsets of {1,...,a} to vertices of G such that sets assigned to adjacent vertices are disjoint. We first show that for every triangle-free planar graph G and a vertex x∈V(G), the graph G has a set coloringφ of G by subsets of {1,...,6} such that |φ(v)|≤ 2 for v∈V(G) and |φ(x)|=3. As a corollary, every triangle-free planar graph on n vertices is (6n:2n+1)-colorable. We further use this result to prove that for every⊿, there exists a constant M⊿ such that every planar graph G of girth at least five and maximum degree⊿ is (6M⊿:2M⊿+1)-colorable. Consequently, planar graphs of girth at least five with bounded maximum degree⊿ have fractional chromatic number at most 3-3/(2M⊿+1).

报告人简介：胡小兰，华中师范大学数学与统计学学院副教授。2015年于南京大学获理学博士学位。2013年9月至2013年12月在美国西弗吉尼亚大学进行短期学术访问，2017年3月至2018年9月在捷克查理大学交流访问。主持国家自然科学基金青年项目，面上项目以及湖北省自然科学基金青年项目各1项，已发表SCI检索论文二十余篇。