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Graphs and Combinatorics

, Volume 33, Issue 4, pp 653–664 | Cite as

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

  • Liliana Alcón
  • Flavia Bonomo
  • María Pía Mazzoleni
Original Paper

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.

Keywords

Vertex intersection graphs Paths on a grid Forbidden induced subgraphs Block graphs 

Notes

Acknowledgements

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

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Copyright information

© Springer Japan 2017

Authors and Affiliations

  • Liliana Alcón
    • 1
  • Flavia Bonomo
    • 2
    • 3
  • María Pía Mazzoleni
    • 4
  1. 1.Departamento de MatemáticaFCE-UNLPLa PlataArgentina
  2. 2.Departamento de Computación, Facultad de Ciencias Exactas y NaturalesUniversidad de Buenos AiresBuenos AiresArgentina
  3. 3.Instituto de Investigación en Ciencias de la Computación (ICC)CONICET-Universidad de Buenos AiresBuenos AiresArgentina
  4. 4.CONICET and Departamento de MatemáticaFCE-UNLPLa PlataArgentina

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