Extremal graphs without four-cycles or five-cycles - Yongqi, Sun,; Xiaohui, Lin,; Yuansheng, Yang,; Lei, Shi, (Utilitas Mathematica, 2009)
Given a set of graphs Ψ = {G1, G2, ⋯, Gk}, let ex(n; Ψ) denote the greatest size of a graph with order n that contains no subgraph isomorphic to any Gi, 1 ≤ i ≤ k. Clapham and Yang Yuansheng investigated the values of ex(n, Ψ) for Ψ = C4(Journal of Graph Theory, 13 (1989), 29-47 and Utilitas Mathematics, 41 (1992), 204-210) and ex(n,Ψ) for Ψ = {C 3,C4, C5}(Utilitas Mathematica, 66 (2004), 249-265). Garnick investigated them for Ψ = {C3, C 4}(Journal of Graph Theory, 17 (1993), 633-645). This paper investigates the values of ex(n, Ψ) for Ψ = {C4, C 5}, n ≤ 21.