Name
Title | ||
|---|---|---|
On the bend number of circular-arc graphs as edge intersection graphs of paths on a grid |
Abstract | ||
|---|---|---|
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. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1016/j.dam.2016.08.004 | Discrete Applied Mathematics |
Keywords | Field | DocType |
Edge intersection graphs,Paths on a grid,Forbidden induced subgraphs,(normal, Helly) circular-arc graphs,Powers of cycles | Block graph,Discrete mathematics,Combinatorics,Indifference graph,Chordal graph,Cograph,Pathwidth,1-planar graph,Mathematics,Trapezoid graph,Split graph | Journal |
Volume | ISSN | Citations |
234 | 0166-218X | 4 |
PageRank | References | Authors |
0.45 | 14 | 7 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Liliana Alcón | 1 | 59 | 14.43 |
| Flavia Bonomo | 2 | 226 | 28.95 |
| Guillermo Durán | 3 | 296 | 29.28 |
| Marisa Gutierrez | 4 | 41 | 12.90 |
| M. P. Mazzoleni | 5 | 12 | 4.05 |
| Bernard Ries | 6 | 176 | 28.68 |
| Mario Valencia-Pabon | 7 | 106 | 15.57 |