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Geometric Intersection Graphs: Do Short Cycles Help?

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Computing and Combinatorics (COCOON 2007)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4598))

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Abstract

Geometric intersection graphs are intensively studied both for their practical motivation and interesting theoretical properties. Many such classes are hard to recognize. We ask the question if imposing restrictions on the girth (the length of a shortest cycle) of the input graphs may help in finding polynomial time recognition algorithms. We give examples in both directions. First we present a polynomial time recognition algorithm for intersection graphs of polygons inscribed in a circle for inputs of girth greater than four (the general recognition problem is NP-complete). On the other hand, we prove that recognition of intersection graphs of segments in the plane remains NP-hard for graphs with arbitrarily large girth.

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Authors and Affiliations

  1. Department of Applied Mathematics, Charles University, Malostranské nám. 25, 118 00  Praha 1, Czech Republic

    Jan Kratochvíl & Martin Pergel

Authors
  1. Jan Kratochvíl
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  2. Martin Pergel
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Guohui Lin

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Kratochvíl, J., Pergel, M. (2007). Geometric Intersection Graphs: Do Short Cycles Help?. In: Lin, G. (eds) Computing and Combinatorics. COCOON 2007. Lecture Notes in Computer Science, vol 4598. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73545-8_14

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  • DOI: https://doi.org/10.1007/978-3-540-73545-8_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73544-1

  • Online ISBN: 978-3-540-73545-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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