A cograph is a graph which does not contain any induced path on four vertices. In this paper, we characterize those cographs that are intersection graphs of paths on a grid in the following two cases: (i) the paths on the grid all have at most one bend and the intersections concern edges (→ B1-EPG); (ii) the paths on the grid are not bended and the intersections concern vertices (→ B0-VPG). In both cases, we give a characterization by a family of forbidden induced subgraphs. We further present linear-time algorithms to recognize B1-EPG cographs and B0-VPG cographs using their cotree.
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- Induced subgraph
- Intersection graph
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics
- Applied Mathematics