科研之友
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摘要
Given a graph H and a positive integer n, the Tur & aacute;n number of H for the order n, denoted by ex(n, H), is the maximum size of a simple graph of order n not containing H as a subgraph. The book with p pages, denoted by Bp, is the graph that consists of p triangles sharing a common edge. Bollob & aacute;s and Erd & oacute;s initiated the research on the Tur & aacute;n number of book graphs in 1975. The two numbers ex(p + 2, Bp) and ex(p + 3, B-p) have been determined by Qiao and Zhan. In this paper we determine the numbers ex(p + 4, B-p), ex(p +5, B-p) and ex(p +6, Bp), and characterize the corresponding extremal graphs for the numbers ex(n, Bp) with n = p + 2, p + 3, p + 4, p+5.
