Title: The Turán number of blow-ups of graphs

Speaker: Liying Kang (Shanghai University)

Abstract：

The blow-up of a graph H is the graph obtained from replacing each edge in H by a clique of the same size where the new vertices of the cliques are all different. Given a graph H and a positive integer n, the extremal number, ex(n;H), is the maximum number of edges in a graph on n vertices that does not contain H as a subgraph. A keyring C_s(k) is a (k + s)-edge graph obtained from a cycle of length k by appending s leaves to one of its vertices. In this talk we determine the extremal number and find the extremal graphs for the blow-ups of keyrings C_s(k) (k≥3, s≥1) when n is sufficiently large. For special cases when k = 0 or s = 0, the extremal number of the blow-ups of the graph C_s(0) (a star) has been determined by Erdős et al. [Erdős et al., J. Comb. Theory, Ser. B. 64 (1995) 89-100] and Chen et al. [Chen et al., J. Comb. Theory, Ser. B. 89 (2003) 159-171], while the extremal number and extremal graphs for the blow-ups of the graph C₀(k) (a cycle) when n is sufficiently large has been determined by Liu [Liu, Electron. J. Combin. 20 (2013) #P65].

个人简介：康丽英,上海大学数学系教授，博士生导师。曾获“上海市三八红旗手”，“上海市曙光学者”称号。中国运筹学会常务理事、中国工业与应用数学学会组合图论专业委员会副主任委员、中国数学会组合图论分会理事。担任国际期刊《Discrete Mathematics, Algorithms and Applications》、《Journal of the Operations Research Society of China》、《Communications on Applied Mathematics and Computation》和国内期刊《运筹学学报》编委。在《SIAM Discrete Mathematics》、《Journal of Graph Theory》、《European Journal of Combinatorics》等学术期刊上发表学术论文140篇，主持完成5项国家自然科学基金项目。曾在美国南卡莱罗纳大学、荷兰蒂尔堡大学、法国巴黎十一大等多所大学进行学术访问和合作研究。

邀请人：王光辉教授

时间：2020-11-11, 19:00-20:30

地点:腾讯会议，ID: 292 870 770