2021/08/01 by Jianfeng Hou, Shufei Wu · 1 citation
paper · doi:10.1002/jgt.22717
Abstract A bisection of a graph is a bipartition of its vertex set in which the two classes differ in size by at most one. For a random bisection of a graph with edges, one expects edges spans in one vertex class. Bollobás and Scott asked for conditions that guarantee a bisection in which both classes span at most edges simultaneously. Let be integers with , and let be a graph with minimum degree and edges. In this article, we prove that if contains neither triangle nor as a subgraph, then admits a bisection in which both classes span at most edges. We also consider Max‐Bisections of graphs without and improve a recent result of Hou and Yan.