Extremal Graphs without Topological Complete Subgraphs

Abstract

Abstract.The exact values of the function ex(n; T Kp) are known for 2n+5 3 ≤ p < n (see [Cera, Diánez, and Márquez, SIAM J. Discrete Math., 13 (2000), pp. 295-301]), where ex(n; T Kp) is the maximum number of edges of a graph of order n not containing a subgraph homeomorphic to the complete graph of order p. In this paper, for 2n+6 3 ≤ p < n − 3, we characterize the family of extremal graphs EX(n; T Kp), i.e., the family of graphs with n vertices and ex(n; T Kp) edges not containing a subgraph homeomorphic to the complete graph of order p.

New exact values of the maximum size of graphs free of topological complete subgraphs

“…More precisely we prove the following two theorems. [3,4] 3n + 2 4 p < n n 2 − (2n − 2p + 1) [3,4] Next F r stands for the family of graphs with r vertices consisting of the disjoint union of cycles.…”