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Sparsely intersecting perfect matchings in cubic graphs

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Abstract

In 1971, Fulkerson made a conjecture that every bridgeless cubic graph contains a family of six perfect matchings such that each edge belongs to exactly two of them; equivalently, such that no three of the matchings have an edge in common. In 1994, Fan and Raspaud proposed a weaker conjecture which requires only three perfect matchings with no edge in common. In this paper we discuss these and other related conjectures and make a step towards Fulkerson’s conjecture by proving the following result: Every bridgeless cubic graph which has a 2-factor with at most two odd circuits contains three perfect matchings with no edge in common.

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References

  1. D. Král’, E. Máčajová, O. Pangrác, A. Raspaud, J.-S. Sereni and M. Škoviera: Projective, affine, and abelian colourings of cubic graphs, European J. Combin. 30 (2009), 53–69.

    Article  MATH  MathSciNet  Google Scholar 

  2. G. Fan and A. Raspaud: Fulkerson’s Conjecture and circuit covers, J. Combin. Theory Ser. B 61 (1994), 133–138.

    Article  MATH  MathSciNet  Google Scholar 

  3. D. R. Fulkerson: Blocking and antiblocking pairs of polyhedra, Math. Program. 1 (1971), 168–194.

    Article  MATH  MathSciNet  Google Scholar 

  4. A. Huck and M. Kochol: Five cycle double covers of some cubic graphs, J. Combin. Theory Ser. B 64 (1995), 119–125.

    Article  MATH  MathSciNet  Google Scholar 

  5. T. Kaiser and A. Raspaud: Non-intersecting perfect matchings in cubic graphs (Extended abstract), Electron. Notes Discrete Math. 28 (2007), 293–299.

    Article  MathSciNet  Google Scholar 

  6. T. Kaiser and A. Raspaud: Perfect matchings with restricted intersection in cubic graphs, European J. Combin. 31 (2010), 1307–1315.

    Article  MATH  MathSciNet  Google Scholar 

  7. E. Máčajová and M. Škoviera: Fano colourings of cubic graphs and the Fulkerson Conjecture, Theoret. Comput. Sci. 349 (2005), 112–120.

    Article  MATH  MathSciNet  Google Scholar 

  8. J. Petersen: Die Theorie der reguläaren Graphen, Acta Math. 15 (1891), 193–220.

    Article  MATH  MathSciNet  Google Scholar 

  9. P. D. Seymour: On multi-colourings of cubic graphs, and conjectures of Fulkerson and Tutte, Proc. London Math. Soc. 38 (1979), 423–460.

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Faculty of Mathematics, Physics and Informatics, Comenius University, 842 48, Bratislava, Slovakia

    Edita Máčajová & Martin Škoviera

Authors
  1. Edita Máčajová
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  2. Martin Škoviera
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Correspondence to Martin Škoviera.

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Máčajová, E., Škoviera, M. Sparsely intersecting perfect matchings in cubic graphs. Combinatorica 34, 61–94 (2014). https://doi.org/10.1007/s00493-014-2550-4

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  • DOI: https://doi.org/10.1007/s00493-014-2550-4

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