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Improved Complexity Results on k-Coloring P t -Free Graphs

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Mathematical Foundations of Computer Science 2013 (MFCS 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8087))

Abstract

A graph is H-free if it does not contain an induced subgraph isomorphic to H. We denote by P k the path on k vertices. In this paper, we prove that 4-COLORING is NP-complete for P 7-free graphs, and that 5-COLORING is NP-complete for P 6-free graphs. The second result is the first NP-completeness shown for any k-COLORING of P 6-free graphs. These two results improve two previously best results and almost complete the classification of complexity of k-COLORING P t -free graphs for k ≥ 4 and t ≥ 1, leaving as the only missing case 4-COLORING P 6-free graphs. Our NP-completeness results use a general framework, which we show is not sufficient to prove the NP-completeness of 4-COLORING P 6-free graphs. We expect that 4-COLORING is polynomial solvable for P 6-free graphs.

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Authors and Affiliations

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

    Shenwei Huang

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  1. Shenwei Huang
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Editor information

Editors and Affiliations

  1. Institute for Science and Technology, 3400, Klosterneuburg, Austria

    Krishnendu Chatterjee

  2. Charles University, 11800, Prague, Czech Republic

    Jirí Sgall

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Huang, S. (2013). Improved Complexity Results on k-Coloring P t -Free Graphs. In: Chatterjee, K., Sgall, J. (eds) Mathematical Foundations of Computer Science 2013. MFCS 2013. Lecture Notes in Computer Science, vol 8087. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40313-2_49

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  • DOI: https://doi.org/10.1007/978-3-642-40313-2_49

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40312-5

  • Online ISBN: 978-3-642-40313-2

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