Extremal numbers of disjoint triangles in r-partite graphs

08/02/2022

∙

by   Junxue Zhang, et al.

∙

0

∙

share

For two graphs G and F, the extremal number of F in G, denoted by ex(G,F), is the maximum number of edges in a spanning subgraph of G not containing F as a subgraph. Determining ex(K_n,F) for a given graph F is a classical extremal problem in graph theory. In 1962, Erdős determined ex(K_n,kK_3), which generalized Mantel's Theorem. On the other hand, in 1974, Bollobős, Erdős, and Straus determined ex(K_n_1,n_2,…,n_r,K_t), which extended Turán's Theorem to complete multipartite graphs. As a generalization of above results, in this paper, we determine ex(K_n_1,n_2,…,n_r,kK_3) for r≥ 5 and 15k≤ n_1+4k≤ n_2≤ n_3≤⋯≤ n_r.