## Abstract

The edge intersection graphs of paths on a grid (or EPG graphs) are graphs whose vertices can be represented as simple paths 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. We consider the case of single-bend paths and its subclass of ⌞-shaped paths, namely, the classes known as B_{1}-EPG and ⌞-EPG graphs, respectively. We show that fully-subdivided graphs are ⌞-EPG graphs, and later use this result in order to show that the following problems are APX-hard on ⌞-EPG graphs: MINIMUM VERTEX COVER, MAXIMUM INDEPENDENT SET, and MAXIMUM WEIGHTED INDEPENDENT SET, and also that MINIMUM DOMINATING SET is NP-complete on ⌞-EPG graphs. We also observe that MINIMUM COLORING is NP-complete already on ⌞-EPG, which follows from a proof for B_{1}-EPG in Epstein et al. (2013). Finally, we provide efficient constant-factor-approximation algorithms for each of these problems on B_{1}-EPG graphs.

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

Pages (from-to) | 224-228 |

Number of pages | 5 |

Journal | Discrete Applied Mathematics |

Volume | 281 |

DOIs | |

State | Published - 15 Jul 2020 |

### Bibliographical note

Publisher Copyright:© 2019 Elsevier B.V.

## Keywords

- B1-EPG graphs
- Edge intersection graph
- Fully-subdivided graphs
- Paths on a grid
- k-simplicial graphs

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

## Fingerprint

Dive into the research topics of 'Hardness and approximation for L-EPG and B_{1}-EPG graphs'. Together they form a unique fingerprint.