On the signed chromatic number of some classes of graphs

A signed graph (G,?) is a G along with function ?:E(G)?{+,?}. closed walk of positive (resp., negative) if it has an even odd) number negative edges, counting repetitions. homomorphism (simple) to another vertex-mapping that preserves adjacencies and signs walks. The chromatic the minimum vertices |V(H)| (H,?) which admits homomorphism. Homomorphisms graphs have been attracting growing attention in last decades, especially due their strong connections theories coloring minors. These homomorphisms particularly studied through scope number. In this work, we provide new results bounds on several families (planar graphs, triangle-free planar Kn-minor-free bounded-degree graphs).