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arXiv · 1907.05257

Recognizing Stick Graphs with and without Length Constraints

Steven Chaplick·Philipp Kindermann·Andre Löffler·Florian Thiele·Alexander Wolff·Alexander Zaft·Johannes Zink
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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.

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Steven Chaplick, Philipp Kindermann, Andre Löffler, Florian Thiele, Alexander Wolff, Alexander Zaft, Johannes Zink. 2019-07-11. Recognizing Stick Graphs with and without Length Constraints. https://doi.org/10.7155/jgaa.00443

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