A Note on Not-4-List Colorable Planar Graphs
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The Four Color Theorem states that every planar graph is properly 4-colorable. Moreover, it is well known that there are planar graphs that are non-$4$-list colorable. In this paper we investigate a problem combining proper colorings and list colorings. We ask whether the vertex set of every planar graph can be partitioned into two subsets where one subset induces a bipartite graph and the other subset induces a $2$-list colorable graph. We answer this question in the negative strengthening the result on non-$4$-list colorable planar graphs.
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2021 ◽
Vol vol. 23, no. 3
(Graph Theory)
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2007 ◽
Vol 44
(3)
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pp. 411-422
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