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Latin American Symposium on Theoretical Informatics

LATIN 2018: LATIN 2018: Theoretical Informatics pp 361–375Cite as

On Split \(B_1\)-EPG Graphs

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10807))

Abstract

In this paper, we are interested in edge intersection graphs of paths in a grid, such that each such path has at most one bend. These graphs were introduced in [12] and they are called \(B_1\)-EPG graphs. In particular, we focus on split graphs and characterise those that are \(B_1\)-EPG. This characterisation allows us to disprove a conjecture of Cameron et al. [7]. The existence of polynomial-time recognition algorithm for this graph class is still unknown. We furthermore investigate inclusion relationships among subclasses of split graphs that are \(B_1\)-EPG.

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References

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Acknowledgements

The first author has been supported by the Scientific and Technological Research Council of Turkey (TÜBİTAK) under 2214-A Doctoral Research Program Grant during his stay in Switzerland. This work was done while the first and second authors visited the University of Fribourg, Switzerland. The support of the institution is gratefully acknowledged.

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Authors and Affiliations

  1. Duzce University, Duzce, Turkey

    Zakir Deniz

  2. ENS Paris Saclay, Paris, France

    Simon Nivelle

  3. University of Fribourg, Fribourg, Switzerland

    Bernard Ries

  4. Geneva School of Business Administration, Geneva, Switzerland

    David Schindl

Authors
  1. Zakir Deniz
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  2. Simon Nivelle
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  3. Bernard Ries
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  4. David Schindl
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Corresponding author

Correspondence to Zakir Deniz .

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Editors and Affiliations

  1. Stony Brook University, Stony Brook, New York, USA

    Michael A. Bender

  2. Rutgers University, New Brunswick, New Jersey, USA

    Martín Farach-Colton

  3. Pace University, New York, New York, USA

    Miguel A. Mosteiro

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Deniz, Z., Nivelle, S., Ries, B., Schindl, D. (2018). On Split \(B_1\)-EPG Graphs. In: Bender, M., Farach-Colton, M., Mosteiro, M. (eds) LATIN 2018: Theoretical Informatics. LATIN 2018. Lecture Notes in Computer Science(), vol 10807. Springer, Cham. https://doi.org/10.1007/978-3-319-77404-6_27

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  • DOI: https://doi.org/10.1007/978-3-319-77404-6_27

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-77403-9

  • Online ISBN: 978-3-319-77404-6

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