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 B₀-VPG graphs. Recognizing this class is an NP-complete problem. Although, there exists a polynomial time algorithm for recognizing chordal B₀-VPG graphs. In this paper, we present a minimal forbidden induced subgraph characterization of B₀-VPG graphs restricted to block graphs. As a byproduct, the proof of the main theorem provides an alternative certifying recognition and representation algorithm for B₀-VPG graphs in the class of block graphs.