Steiner, Raphael A note on graphs of dichromatic number 2. (English) Zbl 1464.05167 Discrete Math. Theor. Comput. Sci. 22, No. 4, Paper No. 11, 8 p. (2020). Summary: Neumann-Lara and Škrekovski conjectured that every planar digraph is 2-colourable. We show that this conjecture is equivalent to the more general statement that all oriented \(K_5\)-minor-free graphs are 2-colourable. Cited in 1 Document MSC: 05C20 Directed graphs (digraphs), tournaments 05C15 Coloring of graphs and hypergraphs 05C10 Planar graphs; geometric and topological aspects of graph theory 05C83 Graph minors Keywords:directed graphs; acyclic colouring; dichromatic number; planar graphs; K5-minor-free graphs Citations:Zbl 1041.05026 PDFBibTeX XMLCite \textit{R. Steiner}, Discrete Math. Theor. Comput. Sci. 22, No. 4, Paper No. 11, 8 p. (2020; Zbl 1464.05167) Full Text: DOI arXiv Link References: [1] URLhttps://doi.org/10.1007/BF01594196. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.