On homomorphisms of planar signed graphs to signed projective cubes

International audienceWe conjecture that every planar signed bipartite graph of unbalanced girth 2g admits a homomorphism to the signed projective cube of dimension 2g - 1. 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-colorabl