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Vertex Intersection Graphs of Paths on a Grid: Characterization Within Block Graphs

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Abstract

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.

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Acknowledgements

We want to thank the anonymous referee for his/her suggestions to improve the writing of this manuscript.

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Authors and Affiliations

  1. Departamento de Matemática, FCE-UNLP, La Plata, Argentina

    Liliana Alcón

  2. Departamento de Computación, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Buenos Aires, Argentina

    Flavia Bonomo

  3. Instituto de Investigación en Ciencias de la Computación (ICC), CONICET-Universidad de Buenos Aires, Buenos Aires, Argentina

    Flavia Bonomo

  4. CONICET and Departamento de Matemática, FCE-UNLP, La Plata, Argentina

    María Pía Mazzoleni

Authors
  1. Liliana Alcón
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  2. Flavia Bonomo
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  3. María Pía Mazzoleni
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Corresponding author

Correspondence to Flavia Bonomo.

Additional information

This work was partially supported by UBACyT Grant 20020130100808BA, CONICET PIP 122-01001-00310 and 112-201201-00450CO and ANPCyT PICT 2012-1324 and 2015-2218 (Argentina).

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

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  • DOI: https://doi.org/10.1007/s00373-017-1791-6

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