Geodesic
Homomorphisms of planar signed graphs to signed projective cubes
Discrete mathematics & theoretical computer science, Tome 15 (2013) no. 3.

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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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     author = {Naserasr, Reza and Rollova, Edita and Sopena, Eric},
     title = {Homomorphisms of planar signed graphs to signed projective cubes},
     journal = {Discrete mathematics & theoretical computer science},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.612/}
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Naserasr, Reza; Rollova, Edita; Sopena, Eric. Homomorphisms of planar signed graphs to signed projective cubes. Discrete mathematics & theoretical computer science, Tome 15 (2013) no. 3. doi : 10.46298/dmtcs.612. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.612/

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