报告主题：平面图的列表4-染色（List 4-colouring of planar graphs）

报 告 人：朱绪鼎 教授（浙江师范大学）

报告时间：2022年4月1日（周五） 10:30

参会方式：腾讯会议

会议ID：924-840-712

邀请人：康丽英

主办部门：理学院数学系

报告摘要：It is known that there are planar graphs G and 4-list assignments L of G such that G is not L-colourable. A natural direction of research is to put restrictions on the list assignments so that for any planar graph G and any 4-list assignment L of G satisfying the restrictions, G is L-colourable. One direction of research is to consider lists with separation. A (k,s)-list assignment of G is a k-list assignment of G with ∣L(x)∩L(y)∣ ≥ s for each edge xy. A graph G is called (k,s)-choosable if G is L-colourable for any (k,s)-list assignment L of G. Mirzakhani constructed a planar graph G which is not (4,3)-choosable and Kratochv´ıl, Tuza and Voigt proved that for any planar graph is (4,2)-choosable. A natural question (asked by Kratochv´ıl, Tuza and Voigt ) is whether every planar graph is (4,2)-choosable.This question received a lot of attention, but there were not much progress on the question itself. Recently, I have answered this quesiton in the affirmative. In this lecture, I shall sketch the proof.