On edge intersection graphs of paths with 2 bends
Discrete Mathematics
2017-11-15 v1 Combinatorics
Abstract
An EPG-representation of a graph is a collection of paths in a plane square grid, each corresponding to a single vertex of , 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.
Cite
@article{arxiv.1711.05096,
title = {On edge intersection graphs of paths with 2 bends},
author = {Martin Pergel and Paweł Rzążewski},
journal= {arXiv preprint arXiv:1711.05096},
year = {2017}
}