A Theory of Rectangularly Dualizable Graphs
Abstract
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, Ko\'zmi\'nski 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.
Keywords
Cite
@article{arxiv.2102.05304,
title = {A Theory of Rectangularly Dualizable Graphs},
author = {Vinod Kumar and Krishnendra Shekhawat},
journal= {arXiv preprint arXiv:2102.05304},
year = {2021}
}