题目: Some Topics on Spectral Extremal Graph Theory

报告人：宁博（天津大学）

时间: 2015年3月23日, 周一   下午15:00-16:30

地点：管研楼1611

摘要： Spectral extremal graph theory is a beautiful branch of graph theory which have attracted much attentions recent decades. In particular, the following Tur/'{a}n-Brudali-Solheid-type problems are considered in this talk: for a given graph $H$, what is $/max/{/rho(G): G~/mbox contains~no~H,v(G)=n/}$? We will briefly survey some interesting and basic theorems in this area, such as spectral analogues of Mantel's theorem on triangle, Tur/'{a}n's theorem on clique, Ore's theorem on Hamilton cycle, Bollob/'{a}s' theorem on pancyclicity, Reidei's theorem on quadrangle, Erd/"{o}s' conjecture on even cycle and etc. Besides, we will also compare these results with the corresponding Tur/'{a}n-type theorems in extremal graph theory. In particular, some of our recent works on spectral analogues of classical theorems on Hamilon cycles (Erd/"{o}s (1962), Moon and Moser (1963), Matthews and Sumner (1985)) will be presented. The main tools involve kinds of closure theories, Tur/'{a}n's theorem, solutions to Zarankiewicz problem and spectral inequalities. (Some results are based on recent joint works with Dr. Jun Ge (LMA, 2015) and Dr. Binlong Li (Preprints, 2015))

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