Abstract
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.
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Research of the first author was supported by the K109240 OTKA grant. Research of the second author was supported by grant no. OTKA 108947 of the Hungarian Scientific Research Fund and by the János Bolyai Research Scholarship of the Hungarian Academy of Sciences.
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Fleiner, T., Wiener, G. Coloring signed graphs using DFS. Optim Lett 10, 865–869 (2016). https://doi.org/10.1007/s11590-015-0962-8
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DOI: https://doi.org/10.1007/s11590-015-0962-8