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 tted 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 areauniversal
rectangular dual. We also present a polynomial time algorithm for
its construction.