Homomorphisms of signed bipartite graphs

International audienceWe study the homomorphism relation between signed graphs where the underlying graph G is bipartite. We show that this notion captures the notions of chromatic number and graph homomorphisms. In particular we will study Hadwiger's conjecture in this setting. We show that for small values of the chromatic number there are natural strengthening of this conjecture but such extensions will not work for larger chromatic numbers