Coloring signed graphs using DFS.

We show that depth first search can be used to give a proper coloring of connected signed graphs G using at most $$\Delta (G)$$ colors, provided G is different from a balanced complete graph, a balanced cycle of odd length, and an unbalanced cycle of even length, thus giving a new, short proof to the generalization of Brooks' theorem to signed graphs, first proved by Máčajová, Raspaud, and Škoviera. [ABSTRACT FROM AUTHOR]