Vertex Intersection Graphs of Paths on a Grid: Characterization Within Block Graphs
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We investigate graphs that can be represented as vertex intersections of horizontal and vertical paths in a grid, the so called \(B_0\)-VPG graphs. Recognizing this class is an NP-complete problem. Although, there exists a polynomial time algorithm for recognizing chordal \(B_0\)-VPG graphs. In this paper, we present a minimal forbidden induced subgraph characterization of \(B_0\)-VPG graphs restricted to block graphs. As a byproduct, the proof of the main theorem provides an alternative certifying recognition and representation algorithm for \(B_0\)-VPG graphs in the class of block graphs.
KeywordsVertex intersection graphs Paths on a grid Forbidden induced subgraphs Block graphs
We want to thank the anonymous referee for his/her suggestions to improve the writing of this manuscript.