报告题目：Some results and problems on unique-maximum colorings of planegraphs

报告简介：A unique-maximum coloring of a plane graph G is a proper vertexcoloring by natural numbers such that each face of G satisfies the property: themaximal color that appears on, appears precisely on one vertex of (or shortly, the maximal color on every face is unique on that face). Fabrici and Göring provedthat six colors are enough for any plane graph and conjectured that four colorssuffice. Thus, this conjecture is a strengthening of the Four Color Theorem.Wendland later decreased the upper bound from six to five. We first show that the conjecture holds for various subclasses of planar graphs but then we disprove itfor planar graphs in general. Thus, the facial unique-maximum chromatic number of the sphere is not four but five. In the second part of the talk, we will considervarious new directions and open problems.

报告人：Riste Škrekovski教授，斯洛文尼亚卢布尔雅那大学

报告时间：2019年07月09日（星期二）下午 1:00

报告地点：扬州大学瘦西湖校区数学科学学院38号楼108报告厅

主办单位：扬州大学数学科学学院

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