Reza Naserasr ; Edita Rollova ; Eric Sopena - Homomorphisms of planar signed graphs to signed projective cubes

dmtcs:612 - Discrete Mathematics & Theoretical Computer Science, September 26, 2013, Vol. 15 no. 3 - https://doi.org/10.46298/dmtcs.612
Homomorphisms of planar signed graphs to signed projective cubes

Authors: Reza Naserasr ; Edita Rollova ; Eric Sopena

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.


Volume: Vol. 15 no. 3
Published on: September 26, 2013
Accepted on: June 9, 2015
Submitted on: February 25, 2013
Keywords: homomorphism,planar signed graph,projective cube,signed graph,[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]


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