2021/02/10 by Vinod Kumar, Kumar, Vinod, Krishnendra Shekhawat +1
Computer Science · #Advanced Graph Theory Research #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Model-Driven Software Engineering Techniques
paper · pdf · doi:10.48550/arxiv.2102.05304
openalex publication_date 2021/02/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A plane graph is called a rectangular graph if each of its edges can be oriented either horizontally or vertically, each of its interior regions is a four-sided region and all interior regions can be fitted in a rectangular enclosure. Only planar graphs can be dualized. If the dual of a plane graph is a rectangular graph, then the plane graph is a rectangularly dualizable graph. In 1985, Koźmiński and Kinnen presented a necessary and sufficient condition for the existence of a rectangularly dualizable graph for a separable connected plane graph. In this paper, we present a counter example for which the conditions given by them for separable connected plane graphs fail and hence, we derive a necessary and sufficient condition for a plane graph to be a rectangularly dualizable graph.