报告题目：

1.On facial unique-maximum colorings

2.Several classes of digraphs

报告人：

1.Riste Škrekovski， 斯洛文尼亚 卢布尔雅那大学 教授

2.Yubao Guo, 德国 亚琛工业大学 教授

报告摘要：

1.A facial unique-maximum coloring of a plane graph is a vertex coloring where on each face the maximal color appears exactly once on the vertices of . If the coloring is required to be proper, then the upper bound for the minimal number of colors required for such a coloring is set to 5. I. Fabrici and F. Göring in 2016 even conjectured that 4 colors always suffice. Confirming the conjecture would hence give a considerable strengthening of the Four Color Theorem. In this talk, we will show that the conjecture holds for subcubic plane graphs, outerplane graphs and plane quadrangulations. Additionally, we willconsider the facial edge-coloring analogue of the aforementioned coloring and show that every 2-connected plane graph admits such a coloring with at most 4 colors. At the end we disprove the aforementioned conjecture.

(Joint work with Vesna Andova, Bernard Lidický, and Borut Lužar, K. Messerschmidt)

2.We introduce several classes of digraphs, which are generalizations of tournaments,e. g. locally semicomplete digraphs, multipartite tournaments, hypertournaments,ect. In this talk, we summarize some cycle structures of such digraphs.

报告地点：数学科学学院38号楼103报告厅

报告时间：9月22日（周五）上午9:30-11:30

欢迎广大师生参加！