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 [12] proved that every graph can be represented as the edge intersection graph of paths on a grid (EPG graph), i.e., one can associate with each vertex of the graph a nontrivial path on a rectangular grid such that two vertices are adjacent if and only if the correspond...

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Detalles Bibliográficos
Autores principales: Alcón, Liliana Graciela, Bonomo, Flavia, Duran, Guillermo Alfredo, Gutiérrez, Marisa, Mazzoleni, María Pía, Ries, Bernard, Valencia-Pabon, Mario
Formato: Articulo Preprint
Lenguaje:Inglés
Publicado: 2018
Materias:
Matemática
(normal, helly) circular-arc graphs
Edge intersection graphs
Forbidden induced subgraphs
Paths on a grid
Powers of cycles
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/95480
https://ri.conicet.gov.ar/11336/83118
https://arxiv.org/abs/1506.08750
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-95480
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Matemática
(normal, helly) circular-arc graphs
Edge intersection graphs
Forbidden induced subgraphs
Paths on a grid
Powers of cycles
spellingShingle Matemática
(normal, helly) circular-arc graphs
Edge intersection graphs
Forbidden induced subgraphs
Paths on a grid
Powers of cycles
Alcón, Liliana Graciela
Bonomo, Flavia
Duran, Guillermo Alfredo
Gutiérrez, Marisa
Mazzoleni, María Pía
Ries, Bernard
Valencia-Pabon, Mario
On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid
topic_facet Matemática
(normal, helly) circular-arc graphs
Edge intersection graphs
Forbidden induced subgraphs
Paths on a grid
Powers of cycles
description Golumbic, Lipshteyn and Stern [12] proved that every graph can be represented as the edge intersection graph of paths on a grid (EPG graph), i.e., one can associate with each vertex of the graph a nontrivial path on a rectangular 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 EPG 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 a B4-EPG graph, by embedding the circle into a rectangle of the grid. In this paper, we prove that circular-arc graphs are B3-EPG, and that there exist circular-arc graphs which are not B2-EPG. If we restrict ourselves to rectangular representations (i.e., the union of the paths used in the model is contained in the boundary of a rectangle of the grid), we obtain EPR (edge intersection of paths in a rectangle) representations. We may define Bk-EPR graphs, k≥0, the same way as Bk-EPG graphs. Circular-arc graphs are clearly B4-EPR graphs and we will show that there exist circular-arc graphs that are not B3-EPR graphs. We also show that normal circular-arc graphs are B2-EPR graphs and that there exist normal circular-arc graphs that are not B1-EPR graphs. Finally, we characterize B1-EPR graphs by a family of minimal forbidden induced subgraphs, and show that they form a subclass of normal Helly circular-arc graphs.
format Articulo
Preprint
author Alcón, Liliana Graciela
Bonomo, Flavia
Duran, Guillermo Alfredo
Gutiérrez, Marisa
Mazzoleni, María Pía
Ries, Bernard
Valencia-Pabon, Mario
author_facet Alcón, Liliana Graciela
Bonomo, Flavia
Duran, Guillermo Alfredo
Gutiérrez, Marisa
Mazzoleni, María Pía
Ries, Bernard
Valencia-Pabon, Mario
author_sort Alcón, Liliana Graciela
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 2018
url http://sedici.unlp.edu.ar/handle/10915/95480
https://ri.conicet.gov.ar/11336/83118
https://arxiv.org/abs/1506.08750
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