报告名称：On the sizes of matchings in 1-planar graphs with high minimum degree

报告专家：黄元秋

专家所在单位：湖南师范大学

报告时间：2022年5月7日14：30-16：30

报告地点:腾讯会议（会议号：494 685 660）

专家简介：黄元秋，湖南师范大学二级教授、博士、博士生导师，教育部“新世纪优秀人才”入选者，湖南省普通高校学科带头人。现为湖南师范大学数学与统计学院副院长、中国组合数学与图论学会理事、中国运筹学会理事、湖南省数学学会常务理事。1996年博士毕业于中国科学院应用数学研究所, 主要从事图论与组合中相关问题的研究，包括图的亏格及最大亏格、图在曲面上的嵌入分布、图的交叉数、图的k-平面性等。在 J. of Combinatorial Theory Ser. B、J. of Graph Theory、Discrete Mathematics、Discrete Applied Mathematics、European J. of Combinatorics、The Electronic J. of Combinatorics、Graphs and Combinatorics以及 《中国科学》等国内外学术期刊上发表论文120余篇。 5次主持完成国家自然科学基金项目，以及省部级科研项目多项。

报告摘要：A matching of a graph is a set of edges without common end vertex. A graph is called 1-planar if it admits a drawing in the plane such that each edge is crossed at most once. Recently, Biedl and Wittnebel proved that every 1-planar graph with minimum degree 3 and n≥7 vertices has a matching of size at least (n+12)/7, and this is tight for some graphs; they also provided tight lower bounds on the matching of sizes for 1-planar graphs with minimum degree 4 and 5. In this paper, we show that any 1-planar graph with minimum degree 6 and n≥32 vertices has a matching of size at least (3n+4)/7, and this lower bound is tight. Our result confirms a conjecture posed by Biedl and Wittnebel in [J. Graph Theory 2022, 99:217-230].