A min–max result on outerplane bipartite graphs

Abstract

An outerplane graph is a connected plane graph with all vertices lying on the boundary of its outer face. For a catacondensed benzenoid graph G , i.e. a 2-connected outerplane graph each inner face of which is a regular hexagon, S. Klavžar and P. Žigert [A min–max result on catacondensed benzenoid graphs, Appl. Math. Lett. 15 (2002) 279–283] discovered that the smallest number of elementary cuts that cover G equals the dimension of a largest induced hypercube of its resonance graph. In this note, we extend the result to any 2-connected outerplane bipartite graph by applying Dilworth’s min–max theorem on partially ordered sets.