## 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

Funding Information:The authors thank Therese Biedl for her advice and insight which lead to a much stronger paper. The third author would also like to thank Manu Basavaraju and Mathew Francis for many helpful discussions. The authors wish to thank the School of Computer Science and Engineering at the Hebrew University of Jerusalem, where the second author is a visiting professor, for providing its facilities for our research activities.

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.