Maximum Bisections of Graphs Without Adjacent Quadrilaterals

Let Ck be a cycle of length k . Let G be a graph with n vertices, m edges. Lin and Zeng proved that if G has a perfect matching and does not contain C-4 , C-6 and C-2k , then G admits a bisection of size at least m|2 + c(k)m((2k+1)/(2k+2)) and showed that the bound is tight for k E { 3 , 5}. In this paper, we obtain a similar tight result by replacing C-4 with two adjacent C-4's.