Recognizing Stick Graphs with and without Length Constraints
Abstract
Stick graphs are intersection graphs of horizontal and vertical line segments that all touch a line of slope -1 and lie above this line. De Luca et al. [GD'18] considered the recognition problem of stick graphs when no order is given (STICK), when the order of either one of the two sets is given (STICK_A), and when the order of both sets is given (STICK_AB). They showed how to solve STICK_AB efficiently. In this paper, we improve the running time of their algorithm, and we solve STICK_A efficiently. Further, we consider variants of these problems where the lengths of the sticks are given as input. We show that these variants of STICK, STICK_A, and STICK_AB are all NP-complete. On the positive side, we give an efficient solution for STICK_AB with fixed stick lengths if there are no isolated vertices.
Cite
@article{arxiv.1907.05257,
title = {Recognizing Stick Graphs with and without Length Constraints},
author = {Steven Chaplick and Philipp Kindermann and Andre Löffler and Florian Thiele and Alexander Wolff and Alexander Zaft and Johannes Zink},
journal= {arXiv preprint arXiv:1907.05257},
year = {2020}
}