# On edge intersection graphs of paths with 2 bends

Pergel, M and Rzazewski, Pavel Michael
(2016)
*On edge intersection graphs of paths with 2 bends.*
LECTURE NOTES IN ARTIFICIAL INTELLIGENCE, 9941 L.
pp. 207-219.
ISSN 0302-9743
10.1007/978-3-662-53536-3_18

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## Abstract

An EPG-representation of a graph G is a collection of paths in a grid, each corresponding to a single vertex of G, so that two vertices are adjacent if and only if their corresponding paths share infinitely many points. In this paper we focus on graphs admitting EPG-representations by paths with at most 2 bends. We show hardness of the recognition problem for this class of graphs, along with some subclasses. We also initiate the study of graphs representable by unaligned polylines, and by polylines, whose every segment is parallel to one of prescribed slopes. We show hardness of recognition and explore the trade-off between the number of bends and the number of slopes. © Springer-Verlag GmbH Germany 2016.

Item Type: | Article |
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Uncontrolled Keywords: | Graph theory; Trade off; Single vertex; Representation of a graph; Polylines; Intersection graph; hardness; Graphic methods; Economic and social effects |

Subjects: | Q Science > QA Mathematics and Computer Science > QA75 Electronic computers. Computer science / számítástechnika, számítógéptudomány |

Divisions: | Informatics Laboratory |

SWORD Depositor: | MTMT Injector |

Depositing User: | MTMT Injector |

Date Deposited: | 03 Feb 2017 08:50 |

Last Modified: | 03 Feb 2017 08:50 |

URI: | http://eprints.sztaki.hu/id/eprint/9063 |

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