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Computing Maximum Unavoidable Subgraphs Using SAT Solvers

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Theory and Applications of Satisfiability Testing – SAT 2016 (SAT 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9710))

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Abstract

Unavoidable subgraphs have been widely studied in the context of Ramsey Theory. The research in this area focuses on highly structured graphs such as cliques, cycles, paths, stars, trees, and wheels. We propose to study maximum unavoidable subgraphs measuring the size in the number of edges. We computed maximum unavoidable subgraphs for graphs up to order nine via SAT solving and observed that these subgraphs are less structured, although all are bipartite. Additionally, we found large unavoidable bipartite subgraphs up to order twelve. We also present the concept of multi-component unavoidable subgraphs and show that large multi-component subgraphs are unavoidable in small graphs. We envision that maximum unavoidable subgraphs can be exploited using an alternative approach to breaking graph symmetries.

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Notes

  1. 1.

    Currently, our system is not able to prove this property for \(n > 18\) due to out of computational resources.

  2. 2.

    We found multiple maximum unavoidable subgraphs for \(K_9\). Figure 3 (a) shows one of them.

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Acknowledgements

The authors are supported by the National Science Foundation under grant number CCF-1526760 and acknowledge the Texas Advanced Computing Center (TACC) at The University of Texas at Austin for providing grid resources that have contributed to the research results reported within this paper.

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Authors and Affiliations

  1. Department of Computer Science, The University of Texas at Austin, Austin, TX, USA

    C. K. Cuong & M. J. H. Heule

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  1. C. K. Cuong
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  2. M. J. H. Heule
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Correspondence to C. K. Cuong .

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Editors and Affiliations

  1. Aix-Marseille Université, Marseille, France

    Nadia Creignou

  2. Université d'Artois, Lens, France

    Daniel Le Berre

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Cuong, C.K., Heule, M.J.H. (2016). Computing Maximum Unavoidable Subgraphs Using SAT Solvers. In: Creignou, N., Le Berre, D. (eds) Theory and Applications of Satisfiability Testing – SAT 2016. SAT 2016. Lecture Notes in Computer Science(), vol 9710. Springer, Cham. https://doi.org/10.1007/978-3-319-40970-2_13

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  • DOI: https://doi.org/10.1007/978-3-319-40970-2_13

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  • Online ISBN: 978-3-319-40970-2

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