On homomorphisms of planar signed graphs to signed projective cubes
Reza Naserasr, Edita Rollová, Éric Sopena · Scuola Normale Superiore eBooks · 2013
We 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-colorable.