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Extending Partial Representations of Trapezoid Graphs

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Graph-Theoretic Concepts in Computer Science (WG 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10520))

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Abstract

A trapezoid graph is an intersection graph of trapezoids spanned between two horizontal lines. The partial representation extension problem for trapezoid graphs is a generalization of the recognition problem: given a graph G and an assignment \(\xi \) of trapezoids to some vertices of G, can \(\xi \) be extended to a trapezoid intersection model of the entire graph G? We show that this can be decided in polynomial time. Thus, we determine the complexity of partial representation extension for one of the two major remaining classes of geometric intersection graphs for which it has been unknown (circular-arc graphs being the other).

The authors were partially supported by National Science Center of Poland grant 2015/17/B/ST6/01873.

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Authors and Affiliations

  1. Department of Theoretical Computer Science, Faculty of Mathematics and Computer Science, Jagiellonian University, Kraków, Poland

    Tomasz Krawczyk & Bartosz Walczak

Authors
  1. Tomasz Krawczyk
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  2. Bartosz Walczak
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Correspondence to Tomasz Krawczyk .

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Editors and Affiliations

  1. Utrecht University, Utrecht, The Netherlands

    Hans L. Bodlaender

  2. Rheinisch-Westfälische Technische Hochschule Aachen, Aachen, Germany

    Gerhard J. Woeginger

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Krawczyk, T., Walczak, B. (2017). Extending Partial Representations of Trapezoid Graphs. In: Bodlaender, H., Woeginger, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 2017. Lecture Notes in Computer Science(), vol 10520. Springer, Cham. https://doi.org/10.1007/978-3-319-68705-6_27

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  • DOI: https://doi.org/10.1007/978-3-319-68705-6_27

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