Advances and Applications in Discrete Mathematics
Volume 28, Issue 1, Pages 75 - 91
(September 2021) http://dx.doi.org/10.17654/DM028010075 |
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RECTANGULARLY DUALIZABLE GRAPHS: AREA-UNIVERSALITY
Vinod Kumar and 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. If the dual of a plane graph is a rectangular graph, then the plane graph is a rectangularly dualizable graph. A rectangular dual is area-universal if any assignment of areas to each of its regions can be realized by a combinatorially weak equivalent rectangular dual. It is still unknown that there exists no polynomial time algorithm to construct an area-universal rectangular dual for a rectangularly dualizable graph. In this paper, we describe a class of rectangularly dualizable graphs wherein each graph can be realized by an area-universal rectangular dual. We also present a polynomial time algorithm for its construction. |
Keywords and phrases: area-universality, cartogram, rectangularly dualizable graph, rectangular dual, VLSI circuit.
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