On the bend number of circular-arc graphs as edge intersection graphs of 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 ed...
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| Acceso en línea: | http://hdl.handle.net/20.500.12110/paper_15710653_v50_n_p249_Alcon |
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todo:paper_15710653_v50_n_p249_Alcon2023-10-03T16:27:08Z On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid Alcón, L. Bonomo, F. Durán, G. Gutierrez, M. Pía Mazzoleni, M. Ries, B. Valencia-Pabon, M. (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. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar 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 Alcón, L. Bonomo, F. Durán, G. Gutierrez, M. Pía Mazzoleni, M. Ries, B. Valencia-Pabon, M. 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. |
| format |
JOUR |
| author |
Alcón, L. Bonomo, F. Durán, G. Gutierrez, M. Pía Mazzoleni, M. Ries, B. Valencia-Pabon, M. |
| author_facet |
Alcón, L. Bonomo, F. Durán, G. Gutierrez, M. Pía Mazzoleni, M. Ries, B. Valencia-Pabon, M. |
| author_sort |
Alcón, L. |
| 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 |
| url |
http://hdl.handle.net/20.500.12110/paper_15710653_v50_n_p249_Alcon |
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