Bisection of Hamilton Plane Graphs under Girth Constraints

Abstract

A bisection of a graph G is a bipartition V 1 and V2 of V(G) such that ‖V 1| – |V 2‖ ≤ 1. The minimum bisection problem asks for a bisection minimizing e(V 1, V 2), where e(V 1, V 2) is the number of edges joining V 1 and V 2. In this paper, we prove that every Hamilton plane graph G with girth at least 4, |V(G)|=n, admits a bisection V 1, V 2 such that .