Abstract
AbstractA 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.
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