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

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...

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Autores principales: Alcón, L., Bonomo, F., Mazzoleni, M.P.
Formato: JOUR
Materias:
Block graphs
Forbidden induced subgraphs
Paths on a grid
Vertex intersection graphs
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_09110119_v33_n4_p653_Alcon
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id todo:paper_09110119_v33_n4_p653_Alcon
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spelling todo:paper_09110119_v33_n4_p653_Alcon2023-10-03T15:44:38Z Vertex Intersection Graphs of Paths on a Grid: Characterization Within Block Graphs Alcón, L. Bonomo, F. Mazzoleni, M.P. Block graphs Forbidden induced subgraphs Paths on a grid Vertex intersection graphs 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. © 2017, Springer Japan. Fil:Bonomo, F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_09110119_v33_n4_p653_Alcon
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Block graphs
Forbidden induced subgraphs
Paths on a grid
Vertex intersection graphs
spellingShingle Block graphs
Forbidden induced subgraphs
Paths on a grid
Vertex intersection graphs
Alcón, L.
Bonomo, F.
Mazzoleni, M.P.
Vertex Intersection Graphs of Paths on a Grid: Characterization Within Block Graphs
topic_facet Block graphs
Forbidden induced subgraphs
Paths on a grid
Vertex intersection graphs
description 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. © 2017, Springer Japan.
format JOUR
author Alcón, L.
Bonomo, F.
Mazzoleni, M.P.
author_facet Alcón, L.
Bonomo, F.
Mazzoleni, M.P.
author_sort Alcón, L.
title Vertex Intersection Graphs of Paths on a Grid: Characterization Within Block Graphs
title_short Vertex Intersection Graphs of Paths on a Grid: Characterization Within Block Graphs
title_full Vertex Intersection Graphs of Paths on a Grid: Characterization Within Block Graphs
title_fullStr Vertex Intersection Graphs of Paths on a Grid: Characterization Within Block Graphs
title_full_unstemmed Vertex Intersection Graphs of Paths on a Grid: Characterization Within Block Graphs
title_sort vertex intersection graphs of paths on a grid: characterization within block graphs
url http://hdl.handle.net/20.500.12110/paper_09110119_v33_n4_p653_Alcon
work_keys_str_mv AT alconl vertexintersectiongraphsofpathsonagridcharacterizationwithinblockgraphs
AT bonomof vertexintersectiongraphsofpathsonagridcharacterizationwithinblockgraphs
AT mazzolenimp vertexintersectiongraphsofpathsonagridcharacterizationwithinblockgraphs
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