Turán Number of an Induced Complete Bipartite Graph Plus an Odd Cycle

Source abstract

Let k ⩾ 2 be an integer. We show that if s = 2 and t ⩾ 2, or s = t = 3, then the maximum possible number of edges in a C 2 k +1 -free graph containing no induced copy of K s,t is asymptotically equal to ( t − s + 1) 1/ s ( n /2) 2−1/ s except when k = s = t = 2. This strengthens a result of Allen, Keevash, Sudakov and Verstraëte [1], and answers a question of Loh, Tait, Timmons and Zhou [14].