Geodesic
List $2$-arboricity of planar graphs with no triangles at distance less than two
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 211-214.

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It is known that not all planar graphs are $4$-choosable; neither all of them are vertex $2$-arborable. However, planar graphs with no triangles at distance less than two are known to be $4$-choosable (Lam, Shiu, Liu, 2001) and $2$-arborable (Raspaud, Wang, 2008). We give a common extension of these two last results in terms of covering the vertices of a graph by induced subgraphs of variable degeneracy. In particular, we prove that every planar graph with no triangles at distance less than two is list $2$-arborable.
Keywords: planar graph, $4$-choosability, vertex-arboricity. 
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O. V. Borodin; A. O. Ivanova. List $2$-arboricity of planar graphs with no triangles at distance less than two. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 5 (2008), pp. 211-214. http://geodesic.mathdoc.fr/item/SEMR_2008_5_a16/

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