Extremal Graphs for the Suspension of Edge-Critical Graphs - Hou, Jianfeng; Li, Heng; Zeng, Qinghou (The Electronic Journal of Combinatorics, 2024)
The Turán number of a graph H, ex(n,H), is the maximum number of edges in an n-vertex graph that does not contain H as a subgraph. For a vertex v and a multi-set F of graphs, the suspension F+v of F is the graph obtained by connecting the vertex v to all vertices of F for each FF. For two integers k1 and r2, let H_i be a graph containing a critical edge with chromatic number r for any i{1,…,k}, and let H={H_1,…,H_k}+v. In this paper, we determine ex(n, H) and characterize all the extremal graphs for sufficiently large n. This generalizes a result of Chen, Gould, Pfender and Wei on intersecting cliques.