TY - JOUR
T1 - The Turán number of book graphs
AU - Yan, Jingru
AU - Zhan, Xingzhi
N1 - Publisher Copyright:
© The Indian National Science Academy 2023.
PY - 2025/3
Y1 - 2025/3
N2 - Given a graph H and a positive integer n, the Turán 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. Bollobás and Erdős initiated the research on the Turán number of book graphs in 1975. The two numbers ex(p+2,Bp) and ex(p+3,Bp) have been determined by Qiao and Zhan. In this paper we determine the numbers ex(p+4,Bp),ex(p+5,Bp) 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.
AB - Given a graph H and a positive integer n, the Turán 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. Bollobás and Erdős initiated the research on the Turán number of book graphs in 1975. The two numbers ex(p+2,Bp) and ex(p+3,Bp) have been determined by Qiao and Zhan. In this paper we determine the numbers ex(p+4,Bp),ex(p+5,Bp) 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.
KW - Book
KW - Extremal graph
KW - Triangle
KW - Turán number
UR - https://www.scopus.com/pages/publications/85164957464
U2 - 10.1007/s13226-023-00467-2
DO - 10.1007/s13226-023-00467-2
M3 - 文章
AN - SCOPUS:85164957464
SN - 0019-5588
VL - 56
SP - 140
EP - 149
JO - Indian Journal of Pure and Applied Mathematics
JF - Indian Journal of Pure and Applied Mathematics
IS - 1
ER -