Edge Intersection Graphs of L-Shaped Paths in Grids

Details Edge Intersection Graphs of L-Shaped Paths in Grids Edge Intersection Graphs of L-Shaped Paths in Grids

2012-04-25

arxiv.org/abs/1204.5702v1

Computer Science

Discrete Mathematics

Scientific paper

In this paper we continue the study of the edge intersection graphs of single bend paths on a rectangular grid (i.e., the edge intersection graphs where each vertex is represented by one of the following shapes: L,\lceil,\rceil,\rfloor). These graphs, called B_1-EPG graphs, were first introduced by Golumbic et al (2009). We focus on the class [L] (the edge intersection graphs of L-shapes) and show that testing for membership in [L] is NP-complete. We then give a characterization and polytime recognition algorithm for special subclasses of Split \cap [L]. We also consider the natural subclasses of B_1-EPG formed by the subsets of the four single bend shapes (i.e., {L}, {L,\lceil}, {L,\rceil}, {L,\lceil,\rceil} - note: all other subsets are isomorphic to these up to 90 degree rotation). We observe the expected strict inclusions and incomparability (i.e., [L] \subsetneq [L,\lceil], [L,\rceil] \subsetneq [L,\lceil,\rceil] \subsetneq B_1-EPG; also, [L,\lceil] is incomparable with [L,\rceil]).

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