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Vertex colouring, Edge Colouring, List Colouring, Fractional Chromatic Number and other variants of graph colouring problems are all on topic.

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Do planar graphs have an acyclic two-coloring?

G. Chartrand, H.V. Kronk, C.E. Wall showed in "The point-arboricity of a graph" (Israel J. Math., 6 (1968), pp. 169–175) that the vertex-set of any planar graph can be partitioned into three induced f …
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