On the characterization of rectangular duals

Abstract

A rectangular partition is a partition of a rectangle into a finite number of rectangles. A rectangular partition is generic if no four of its rectangles meet at the same point. A plane graph G is called a rectangularly dualizable graph if G can be represented as a rectangular partition such that each vertex is represented by a rectangle in the partition and each edge is represented by a common boundary segment shared by the corresponding rectangles. Then the rectangular partition is called a rectangular dual of the RDG. In this paper, we have found a minor error in a characterization for rectangular duals given by Koźmiński and Kinnen in 1985 without formal proof, and we fix this characterization with formal proof.