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Coloring Graphs without Short Cycles and Long Induced Paths

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Fundamentals of Computation Theory (FCT 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6914))

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Abstract

The girth of a graph G is the length of a shortest cycle in G. For any fixed girth g ≥ 4 we determine a lower bound ℓ(g) such that every graph with girth at least g and with no induced path on ℓ(g) vertices is 3-colorable. In contrast, we show the existence of an integer ℓ such that testing for 4-colorability is NP-complete for graphs with girth 4 and with no induced path on ℓ vertices.

This work has been supported by EPSRC (EP/G043434/1).

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Authors and Affiliations

  1. School of Engineering and Computing Sciences, Science Laboratories, Durham University, South Road, Durham, DH1 3LE, England

    Petr A. Golovach, Daniël Paulusma & Jian Song

Authors
  1. Petr A. Golovach
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  2. Daniël Paulusma
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  3. Jian Song
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Editor information

Editors and Affiliations

  1. Department of Informatics, University of Oslo, Postboks 1080 Blindern, 0316, Oslo, Norway

    Olaf Owe  & Martin Steffen  & 

  2. Department of Informatics, University of Bergen, Postboks 7800, 5020, Bergen, Norway

    Jan Arne Telle

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Golovach, P.A., Paulusma, D., Song, J. (2011). Coloring Graphs without Short Cycles and Long Induced Paths. In: Owe, O., Steffen, M., Telle, J.A. (eds) Fundamentals of Computation Theory. FCT 2011. Lecture Notes in Computer Science, vol 6914. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22953-4_17

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  • DOI: https://doi.org/10.1007/978-3-642-22953-4_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22952-7

  • Online ISBN: 978-3-642-22953-4

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