On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid

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Golumbic, Lipshteyn and Stern proved that every graph can be represented as the edge intersection graph of paths on a grid, i.e., one can associate to each vertex of the graph a nontrivial path on a grid such that two vertices are adjacent if and only if the corresponding paths share at least one ed...

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Detalles Bibliográficos
Autores principales: Bonomo, Flavia, Durán, Guillermo A.
Publicado: 2015
Materias:
(normal, Helly)
Circular-arc graphs
Edge intersection graphs
Forbidden induced subgraphs
Paths on a grid
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15710653_v50_n_p249_Alcon
http://hdl.handle.net/20.500.12110/paper_15710653_v50_n_p249_Alcon
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Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_15710653_v50_n_p249_Alcon
record_format dspace
spelling paper:paper_15710653_v50_n_p249_Alcon2025-07-30T19:00:07Z On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid Bonomo, Flavia Durán, Guillermo A. (normal, Helly) Circular-arc graphs Edge intersection graphs Forbidden induced subgraphs Paths on a grid Golumbic, Lipshteyn and Stern proved that every graph can be represented as the edge intersection graph of paths on a grid, i.e., one can associate to each vertex of the graph a nontrivial path on a grid such that two vertices are adjacent if and only if the corresponding paths share at least one edge of the grid. For a nonnegative integer k, Bk-EPG graphs are defined as graphs admitting a model in which each path has at most k bends. Circular-arc graphs are intersection graphs of open arcs of a circle. It is easy to see that every circular-arc graph is B4-EPG, by embedding the circle into a rectangle of the grid. In this paper we prove that every circular-arc graph is B3-EPG, but if we restrict ourselves to rectangular representations there exist some graphs that require paths with four bends. We also show that normal circular-arc graphs admit rectangular representations with at most two bends per path. Moreover, we characterize graphs admitting a rectangular representation with at most one bend per path by forbidden induced subgraphs, and we show that they are a subclass of normal Helly circular-arc graphs. © 2015 Elsevier B.V. Fil:Bonomo, F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Durán, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2015 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15710653_v50_n_p249_Alcon http://hdl.handle.net/20.500.12110/paper_15710653_v50_n_p249_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 (normal, Helly)
Circular-arc graphs
Edge intersection graphs
Forbidden induced subgraphs
Paths on a grid
spellingShingle (normal, Helly)
Circular-arc graphs
Edge intersection graphs
Forbidden induced subgraphs
Paths on a grid
Bonomo, Flavia
Durán, Guillermo A.
On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
topic_facet (normal, Helly)
Circular-arc graphs
Edge intersection graphs
Forbidden induced subgraphs
Paths on a grid
description Golumbic, Lipshteyn and Stern proved that every graph can be represented as the edge intersection graph of paths on a grid, i.e., one can associate to each vertex of the graph a nontrivial path on a grid such that two vertices are adjacent if and only if the corresponding paths share at least one edge of the grid. For a nonnegative integer k, Bk-EPG graphs are defined as graphs admitting a model in which each path has at most k bends. Circular-arc graphs are intersection graphs of open arcs of a circle. It is easy to see that every circular-arc graph is B4-EPG, by embedding the circle into a rectangle of the grid. In this paper we prove that every circular-arc graph is B3-EPG, but if we restrict ourselves to rectangular representations there exist some graphs that require paths with four bends. We also show that normal circular-arc graphs admit rectangular representations with at most two bends per path. Moreover, we characterize graphs admitting a rectangular representation with at most one bend per path by forbidden induced subgraphs, and we show that they are a subclass of normal Helly circular-arc graphs. © 2015 Elsevier B.V.
author Bonomo, Flavia
Durán, Guillermo A.
author_facet Bonomo, Flavia
Durán, Guillermo A.
author_sort Bonomo, Flavia
title On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
title_short On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
title_full On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
title_fullStr On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
title_full_unstemmed On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
title_sort on the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
publishDate 2015
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15710653_v50_n_p249_Alcon
http://hdl.handle.net/20.500.12110/paper_15710653_v50_n_p249_Alcon
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