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Uniquely edge colourable graphs. (English) Zbl 0599.05023
The aim of this paper is to extend known results concerning the (finite simple) uniquely edge colourable graphs into further classes of graphs. All finite uniquely k-edge colourable graphs (including multigraphs) with \(4\leq k<\aleph_ 0\) are constructed and enumerated. Similarly, all uniquely k-edge colourable graphs with \(k\geq \aleph_ 0\) are described. Cases \(k<3\) and \(k=3\) are considered as well. The results were presented in the author’s paper in Graphs and other combinatorial topics, Proc. 3rd Czech. Symp., Prague 1982, Teubner Texte Math. 59, 17-22 (1983; Zbl 0538.05035).
05C15 Coloring of graphs and hypergraphs
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