The Turán number of book graphs

Jingru Yan () and Xingzhi Zhan ()
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Jingru Yan: East China Normal University
Xingzhi Zhan: East China Normal University

Indian Journal of Pure and Applied Mathematics, 2025, vol. 56, issue 1, 140-149

Abstract: Abstract Given a graph H and a positive integer n, the Turán number of H for the order n, denoted by $$\textrm{ex}(n,H),$$ 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 $$B_p$$ B p , is the graph that consists of p triangles sharing a common edge. Bollobás and Erdős initiated the research on the Turán number of book graphs in 1975. The two numbers $$\textrm{ex}(p+2,B_p)$$ ex ( p + 2 , B p ) and $$\textrm{ex}(p+3,B_p)$$ ex ( p + 3 , B p ) have been determined by Qiao and Zhan. In this paper we determine the numbers $$\textrm{ex}(p+4,B_p),$$ ex ( p + 4 , B p ) , $$\textrm{ex}(p+5,B_p)$$ ex ( p + 5 , B p ) and $$\textrm{ex}(p+6,B_p),$$ ex ( p + 6 , B p ) , and characterize the corresponding extremal graphs for the numbers $$\textrm{ex}(n,B_p)$$ ex ( n , B p ) with $$n=p+2,\,p+3,\,p+4,\,p+5.$$ n = p + 2 , p + 3 , p + 4 , p + 5 .

Keywords: Turán number; Book; Triangle; Extremal graph; 05C35; 05C75 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s13226-023-00467-2

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