2021/01/10 by Vinod Kumar, Kumar, Vinod, Krishnendra Shekhawat +1
Computer Science · #Computational Geometry and Mesh Generation #Model-Driven Software Engineering Techniques #Advanced Graph Theory Research
paper · pdf · doi:10.48550/arxiv.2101.03505
A plane graph is said to be a rectangular graph if each of its edges can be oriented horizontal or vertical, its internal regions are four-sided and it has a rectangular enclosure. If dual of a planar graph is a rectangular graph, then the graph is said to be a rectangular dualizable graph (RDG). In this paper, we present adjacency transformations between RDGs and present polynomial time algorithms for their transformations. An RDG G=(V, E) is called maximal RDG (MRDG) if there does not exist an RDG G'=(V, E') with E' ⊃ E. An RDG G=(V, E) is said to be an edge-reducible if there exists an RDG G'=(V, E') such that E⊃ E'. If an RDG is not edge-reducible, it is said to be an edge-irreducible RDG. We show that there always exists an MRDG for a given RDG. We also show that an MRDG is edge-reducible and can always be transformed to a minimal one (an edge-irreducible RDG).