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A Hajós-like theorem for list coloring. (English) Zbl 0853.05037
G. Hajós [Wiss. Z. Martin Luther Univ., Math.-Natur. Reihe 10, 116-117 (1961)] showed that every graph which is not $$q$$-colorable can be obtained from the complete graph $$K_{q + 1}$$, by a sequence of operations of three types. The present author proves an analogue of this theorem for the list-chromatic number, applying again three operations (two of which agree with those of Hajós; the third is a variant), but now starting with a complete bipartite graph.

##### MSC:
 05C15 Coloring of graphs and hypergraphs
##### Keywords:
list coloring; list-chromatic number
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##### References:
 [1] Erdös, P.; Rubin, A.L.; Taylor, H., Choosability in graphs, (), 122-157 [2] Hajós, G., Über eine konstruktion nicht n-färbbarer graphen, Wiss. Z. martin luther univ. math.-natur. reihe., 10, 116-117, (1961) [3] Mahadev, N.V.R.; Roberts, F.S.; Santhanakrishnan, P., 3-choosable complete bipartite graphs, () [4] Vizing, V.G., Colouring the vertices of a graph in prescribed colours, Diskret. anal., 29, 3-10, (1976), (in Russian)
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