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arXiv · 2102.05304

A Theory of Rectangularly Dualizable Graphs

Vinod Kumar·Krishnendra Shekhawat
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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.

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Vinod Kumar, Krishnendra Shekhawat. 2021-02-10. A Theory of Rectangularly Dualizable Graphs. https://arxiv.org/abs/2102.05304

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