NP-Completeness of Max-Cut for Segment Intersection Graphs

Oswin Aichholzer, Wolfgang Mulzer, Partick Schnider, Birgit Vogtenhuber

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Abstract

We consider the problem of finding a maximum cut in a graph $G = (V, E)$, that is, a partition $ V_1 dotcup V_2$ of $V$ such that the number of edges between $V_1$ and $V_2$ is maximum. It is well known that the decision problem whether $G$ has a cut of at least a given size is in general NP-complete. We show that this problem remains hard when restricting the input to segment intersection graphs. These are graphs whose vertices can be drawn as straight-line segments, where two vertices share an edge if and only if the corresponding segments intersect. We obtain our result by a reduction from a variant of Planar Max-2-SAT that we introduce and also show to be NP-complete.
Original languageEnglish
Title of host publicationProc. $34^th$ European Workshop on Computational Geometry EuroCG '18
Place of PublicationBerlin, Germany
Pages32:1-32:6
Publication statusPublished - 2018

Cite this

Aichholzer, O., Mulzer, W., Schnider, P., & Vogtenhuber, B. (2018). NP-Completeness of Max-Cut for Segment Intersection Graphs. In Proc. $34^th$ European Workshop on Computational Geometry EuroCG '18 (pp. 32:1-32:6). Berlin, Germany.

NP-Completeness of Max-Cut for Segment Intersection Graphs. / Aichholzer, Oswin; Mulzer, Wolfgang; Schnider, Partick; Vogtenhuber, Birgit.

Proc. $34^th$ European Workshop on Computational Geometry EuroCG '18. Berlin, Germany, 2018. p. 32:1-32:6.

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

Aichholzer, O, Mulzer, W, Schnider, P & Vogtenhuber, B 2018, NP-Completeness of Max-Cut for Segment Intersection Graphs. in Proc. $34^th$ European Workshop on Computational Geometry EuroCG '18. Berlin, Germany, pp. 32:1-32:6.
Aichholzer O, Mulzer W, Schnider P, Vogtenhuber B. NP-Completeness of Max-Cut for Segment Intersection Graphs. In Proc. $34^th$ European Workshop on Computational Geometry EuroCG '18. Berlin, Germany. 2018. p. 32:1-32:6
Aichholzer, Oswin ; Mulzer, Wolfgang ; Schnider, Partick ; Vogtenhuber, Birgit. / NP-Completeness of Max-Cut for Segment Intersection Graphs. Proc. $34^th$ European Workshop on Computational Geometry EuroCG '18. Berlin, Germany, 2018. pp. 32:1-32:6
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