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Article Dans Une Revue Discrete Mathematics and Theoretical Computer Science Année : 2013

Homomorphisms of planar signed graphs to signed projective cubes

Résumé

We conjecture that every signed graph of unbalanced girth 2g, whose underlying graph is bipartite and planar, admits a homomorphism to the signed projective cube of dimension 2g1. Our main result is to show that for a given g, this conjecture is equivalent to the corresponding case (k = 2g) of a conjecture of Seymour claiming that every planar k-regular multigraph with no odd edge-cut of less than k edges is k-edge-colorable. To this end, we exhibit several properties of signed projective cubes and establish a folding lemma for planar even signed graphs.
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Dates et versions

hal-00876298 , version 1 (24-10-2013)
hal-00876298 , version 2 (28-03-2014)

Identifiants

  • HAL Id : hal-00876298 , version 2

Citer

Reza Naserasr, Edita Rollova, Eric Sopena. Homomorphisms of planar signed graphs to signed projective cubes. Discrete Mathematics and Theoretical Computer Science, 2013, 15 (3), pp.1-12. ⟨hal-00876298v2⟩
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