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Narrowing the Complexity Gap for Colouring (C s ,P t )-Free Graphs

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Algorithmic Aspects in Information and Management (AAIM 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8546))

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Abstract

Let k be a positive integer. The k-Colouring problem is to decide whether a graph has a k-colouring. The k-Precolouring Extension problem is to decide whether a colouring of a subset of a graph’s vertex set can be extended to a k-colouring of the whole graph. A k-list assignment of a graph is an allocation of a list — a subset of {1,…,k} — to each vertex, and the List k -Colouring problem asks whether the graph has a k-colouring in which each vertex is coloured with a colour from its list. We prove a number of new complexity results for these three decision problems when restricted to graphs that do not contain a cycle on s vertices or a path on t vertices as induced subgraphs (for fixed positive integers s and t).

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Author information

Authors and Affiliations

  1. School of Computing Science, Simon Fraser University, Burnaby, B.C., V5A 1S6, Canada

    Shenwei Huang

  2. School of Engineering and Computing Sciences, Durham University, Science Laboratories, South Road, Durham, DH1 3LE, United Kingdom

    Matthew Johnson & Daniël Paulusma

Authors
  1. Shenwei Huang
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  2. Matthew Johnson
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  3. Daniël Paulusma
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Editor information

Editors and Affiliations

  1. School of Computing Science, Simon Fraser University, V5A 1S6, Burnaby, BC, Canada

    Qianping Gu  & Pavol Hell  & 

  2. Department of Computer Science, University of Regina, S4S 0A2, Regina, SK, Canada

    Boting Yang

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© 2014 Springer International Publishing Switzerland

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Huang, S., Johnson, M., Paulusma, D. (2014). Narrowing the Complexity Gap for Colouring (C s ,P t )-Free Graphs. In: Gu, Q., Hell, P., Yang, B. (eds) Algorithmic Aspects in Information and Management. AAIM 2014. Lecture Notes in Computer Science, vol 8546. Springer, Cham. https://doi.org/10.1007/978-3-319-07956-1_15

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  • DOI: https://doi.org/10.1007/978-3-319-07956-1_15

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-07955-4

  • Online ISBN: 978-3-319-07956-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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