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.
CITATION STYLE
Alcón, L., Bonomo, F., & Mazzoleni, M. P. (2017). Vertex Intersection Graphs of Paths on a Grid: Characterization Within Block Graphs. Graphs and Combinatorics, 33(4), 653–664. https://doi.org/10.1007/s00373-017-1791-6
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