We study kernelizations for Max-Bisection above Tight Lower Bound, which is to decide if a given graph $G=(V,E)$ admits a bisection with at least $\lceil |E|/2\rceil +k$ crossing edges. The best known kernel for this problem has 16k vertices. Based on the Gallai–Edmonds decomposition, we divide the vertices of G into several categories and study the roles of vertices in each category for obtaining a larger number of crossing edges. By making use of the properties of maximum matchings in G, graph G is partitioned into a set of blocks, and each block in G is closely related to the number of crossing edges of a bisection of G. By analyzing the number of crossing edges in blocks, an improved kernel of 8k vertices is presented.

我们研究紧下界上方的最大二分法的核化，这是为了确定给定图$G=（V，Ë）$ 接受至少具有 $\lceil |Ë|/2\rceil +ķ$交叉边缘。这个问题最著名的内核有16 k个顶点。基于Gallai–Edmonds分解，我们将G的顶点分为几个类别，并研究每个类别中顶点的作用以获得更大的交叉边缘。通过利用在最大匹配的属性的ģ，图ģ被划分为一组块，并且在每个块中ģ密切相关的二等分的交叉的边的数目ģ。通过分析块中相交边的数量，提出了一种改进的8 k顶点核。