报告题目1：Degeneracy bounds, stability, and a sharp gap for B-colorings

报告人：胡晓雪副教授，浙江科技大学

报告时间：9月24日（周四）18:30-19:30

报告地点：腾讯会议：360-836-865

报告摘要：A proper edge-coloring of G is called a B-coloring if every 4-cycle of G is colored with four distinct colors. Let qB(G) denote the minimum number of colors needed for a B-coloring of G. Let △2(G) denote the maximum number of common neighbors of two distinct vertices of G. In this talk, I will present the following results. For integers 1≤d≤△, every finite simple d-degenerate graph G with △(G)≤△ satisfies qB(G)≤△+(d-1)△2(G)≤d△. Consequently, d△ is the exact maximum, with equality precisely for graphs containing Kd,△. For △≥3, we further show that every K3,△-free 3-degenerate graph satisfies qB(G)≤3△-2; the example K3,△-1 shows that this bound is best possible up to one.

For loopless multigraphs, we establish a sharp gap in the possible values of qB(G). For every integer △≥3, every finite loopless multigraph G with △(G)≤△ satisfies qB(G)≤△(△-1) unless G has a component isomorphic to K△,△, in which case qB(G)=△2. The bound △(△-1) is attained by both K△, △-1 and K△,△-e. This is joint work with Jiangxu Kong and Yiqiao Wang.

报告人简介：胡晓雪，浙江科技大学副教授，硕士生导师。主要研究方向为图的结构、染色及分解问题，在J. Graph Theory, European J. Combin., SIAM J. Discrete Math., Discrete Math., 《中国科学：数学》等国内外知名期刊上发表论文30余篇。主持完成国家自然科学基金青年基金1项。

报告题目2：1-Planar graphs without 6-cycles are 6-choosable

报告人：吴情琴博士，浙江财经大学

报告时间：9月24日（周四）19:30-20:30

报告地点：腾讯会议：360-836-865

报告摘要：A graph is 1-planar if it can be drawn in the plane so that each edge is crossed by at most one other edge. A graph is k-degenerate if each of its subgraphs contains a vertex of degree at most k. It was known that every 1-planar graph is 8-choosable. In this talk, we show that every 1-planar graph without 6-cycles is 5-degenerate and hence 6-choosable.

报告人简介：吴情琴，博士，毕业于浙江师范大学，现为浙江财经大学数据科学学院讲师。主要从事图的结构参数与染色问题研究，相关研究成果发表于J. Graph Theory, DiscreteAppl.Math.,Czechoslovak Math. J.,《数学进展》等国内外知名期刊。

邀请人：数学研究所