Extremal even-cycle-free subgraphs of the complete transposition graphs

Abstract

Given graphs G and H, the generalized Turán number ex(G,H) is the maximum number of edges in an H-free subgraph of G. In this paper, we obtain an asymptotic upper bound on ex(CTn,C2ℓ) for any n≥3 and ℓ≥2, where C2ℓ is the cycle of length 2ℓ and CTn is the complete transposition graph which is defined as the Cayley graph on the symmetric group Sn with respect to the set of all transpositions of Sn.