## Abstract

We combine the known notion of the edge intersection graphs of paths in a tree with a VLSI grid layout model to introduce the edge intersection graphs of paths on a grid. Let P be a collection of nontrivial simple paths on a grid G. We define the edge intersection graph EPG(P) of P to have vertices which correspond to the members of P, such that two vertices are adjacent in EPG(P) if the corresponding paths in P share an edge in G.An undirected graph G is called an edge intersection graph of paths on a grid (EPG) if G = EPG(P) for some P and G, and (P, G) is an EPG representation of G. We prove that every graph is an EPG graph. A turn of a path at a grid point is called a bend. We consider here EPG representations in which every path has at most a single bend, called B _{1}-EPG representations and the corresponding graphs are called B _{1}-EPG graphs. We prove that any tree is a B_{1}-EPG graph. Moreover, we give a structural property that enables one to generate non B _{1}-EPG graphs. Furthermore, we characterize the representation of cliques and chordless 4-cycles in B_{1}-EPG graphs. We also prove that single bend paths on a grid have Strong Helly number 3.

Original language | English |
---|---|

Pages (from-to) | 130-138 |

Number of pages | 9 |

Journal | Networks |

Volume | 54 |

Issue number | 3 |

DOIs | |

State | Published - Oct 2009 |

## Keywords

- Intersection graphs
- Path bend
- Paths on a grid

## ASJC Scopus subject areas

- Information Systems
- Computer Networks and Communications