A New Kernel for Parameterized Max-Bisection Above Tight Lower Bound

In this paper, we study kernelization of Parameterized Max-Bisection above Tight Lower Bound problem, which is to find a bisection (V-1, V-2) of G with at least inverted right perpendicular vertical bar E vertical bar/2inverted left perpendicular + k crossing edges for a given graph G = (V, E). The current best vertex kernel result for the problem is of size 16k. Based on analysis of the relation between maximum matching and vertices in Gallai-Edmonds decomposition of G, we divide graph G into a set of blocks, and each block in G is closely related to the number of crossing edges of bisection of G. By analyzing the number of crossing edges in all blocks, an improved vertex kernel of size 8k is presented.