| dc.creator | Alcón, Liliana Graciela | |
| dc.creator | Bonomo, Flavia | |
| dc.creator | Duran, Guillermo Alfredo | |
| dc.creator | Gutiérrez, Marisa | |
| dc.creator | Mazzoleni, María Pía | |
| dc.creator | Ries, Bernard | |
| dc.creator | Valencia-Pabon, Mario | |
| dc.date | 2018-01 | |
| dc.date | 2020-05-08T18:54:50Z | |
| dc.date.accessioned | 2023-07-14T20:07:37Z | |
| dc.date.available | 2023-07-14T20:07:37Z | |
| dc.identifier | http://sedici.unlp.edu.ar/handle/10915/95480 | |
| dc.identifier | https://ri.conicet.gov.ar/11336/83118 | |
| dc.identifier | https://arxiv.org/abs/1506.08750 | |
| dc.identifier | issn:0166-218X | |
| dc.identifier.uri | https://repositorioslatinoamericanos.uchile.cl/handle/2250/7438007 | |
| dc.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. | |
| dc.description | Consejo Nacional de Investigaciones Científicas y Técnicas | |
| dc.description | Facultad de Ciencias Exactas | |
| dc.format | application/pdf | |
| dc.format | 12-21 | |
| dc.language | en | |
| dc.rights | http://creativecommons.org/licenses/by-nc-sa/4.0/ | |
| dc.rights | Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) | |
| dc.subject | Matemática | |
| dc.subject | (normal, helly) circular-arc graphs | |
| dc.subject | Edge intersection graphs | |
| dc.subject | Forbidden induced subgraphs | |
| dc.subject | Paths on a grid | |
| dc.subject | Powers of cycles | |
| dc.title | On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid | |
| dc.type | Articulo | |
| dc.type | Preprint | |
