Transformations among rectangular partitions

Abstract

We first prove that there always exists a maximal rectangularly dualizable graph for a given rectangularly dualizable graph and present an algorithm for its construction. Further, we show that a maximal rectangularly dualizable graph can always be transformed to an edge-irreducible rectangularly dualizable graph and present an algorithm that transforms a maximal rectangularly dualizable graph to an edge-irreducible rectangularly dualizable graph.