On colorings and orientations of signed graphs
Copyright policy )On colorings and orientations of signed graphs
Summary: A classical theorem independently due to \textit{T. Gallai} [in: Theory of Graphs, Proc. Colloq. Tihany, Hungary 1966, 115--118 (1968; Zbl 0159.54403)] and \textit{B. Roy} [Rev. Franç. Inform. Rech. Opér. 1, No. 5, 129--132 (1967; Zbl 0157.31302)] states that a graph \(G\) has a proper \(k\)-coloring if and only if \(G\) has an orientation without coherent paths of length \(k\). An analogue of this result for signed graphs is proved in this article.
- University System of Ohio United States
- Wright State University United States
Statistics and Probability, Applied Statistics, Applied Mathematics, Directed graphs (digraphs), tournaments, bidirection, orientation, Signed and weighted graphs, signed graph, Coloring of graphs and hypergraphs, Physical Sciences and Mathematics, QA1-939, Mathematics, signed-graph coloring
Statistics and Probability, Applied Statistics, Applied Mathematics, Directed graphs (digraphs), tournaments, bidirection, orientation, Signed and weighted graphs, signed graph, Coloring of graphs and hypergraphs, Physical Sciences and Mathematics, QA1-939, Mathematics, signed-graph coloring
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