关于不含2Kp+1图的度幂的Turán型问题

关于不含2K_p+1图的度幂的Turán型问题

摘要: 拟在极值图论这一重要的研究分支上研究不含 2K_p+1 图的度幂的Turán型问题。基于2个不含 2K_p+1 的图的度序列，得到关于 2K_p+1 的度幂极图的一些度序列性质，并在此基础上对度幂极图的度进行分类讨论，借助相关引理与Erdös−Gallai定理，证明了当 2p+2\leqslant n\leqslant 2p+4 时不含 2K_p+1 图的度的 q 次幂之和极值，其中 n 是图的顶点个数， p\geqslant 2 ， q\geqslant 2 。

Abstract: In the report, based on the important branch of extremal graph theory, the Turán-type problem for the degree powers of graphs without 2K_p+1 was studied. Based on the degree sequences of two 2K_p+1-free graphs, some degree sequence properties of extremal graph were obtained. Then the degrees of the extremal graph were categorized and discussed. With the help of relevant lemmas and the Erdös-Gallai theorem, when 2p+2≤n≤2p+4, the maximum values of the q-power sum of degrees of 2K_p+1-free graphs were proved, in which n is the number of vertices, p≥2 and q≥2.