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For integers n ≥ 4 and ν ≥ n + 1, let ex(ν; {C3, . . . , Cn}) denote the maximum number of edges in a graph of order ν and girth at least n+1. The {C3, . . . , Cn}-free graphswith order ν and size ex(ν; {C3, . . . , Cn}) are called extremal graphs and denoted by EX(ν; {C3, . . . , Cn}). We prove that given an integer k ≥ 0, for each n ≥ 2 log2(k + 2) there(More)
Let G be a graph with vertex set V = V (G) and edge set E = E(G). The cardinalities of these sets are denoted by |V (G)| = n and |E(G)| = e. Let u and v be two distinct vertices of G. A path from u to v, also called an uv-path in G, is a subgraph P with vertex set V (P ) = {u = x0, x1, . . . , xr = v} and it is usually denoted by P : x0x1 · · ·xr. Two(More)