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Connect Four and Graph Decomposition

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Abstract

We introduce standard decomposition, a natural way of decomposing a labeled graph into a sum of certain labeled subgraphs. We motivate this graph-theoretic concept by relating it to Connect Four decompositions of standard sets. We prove that all standard decompositions can be generated in polynomial time as a function of the combined size of the input and the output. This implies that all Connect Four decompositions can be generated in polynomial time.

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Authors and Affiliations

  1. Département de mathématiques, Faculté des Sciences, Université d’Angers, 2, Boulevard Lavoisier, 49045, Angers Cedex 01, France

    Laurent Evain

  2. Department of Mathematics, Cornell University, Malott Hall, Ithaca, New York, 14853, USA

    Mathias Lederer & Bjarke Hammersholt Roune

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  1. Laurent Evain
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  2. Mathias Lederer
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  3. Bjarke Hammersholt Roune
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Correspondence to Bjarke Hammersholt Roune.

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Evain, L., Lederer, M. & Roune, B.H. Connect Four and Graph Decomposition. comput. complex. 25, 815–848 (2016). https://doi.org/10.1007/s00037-016-0123-1

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  • DOI: https://doi.org/10.1007/s00037-016-0123-1

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