Geodesic
The list linear arboricity of planar graphs
Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 499-510

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The linear arboricity la(G) of a graph G is the minimum number of linear forests which partition the edges of G. An and Wu introduce the notion of list linear arboricity lla(G) of a graph G and conjecture that lla(G) = la(G) for any graph G. We confirm that this conjecture is true for any planar graph having Δ ≥ 13, or for any planar graph with Δ ≥ 7 and without i-cycles for some i ∈ 3,4,5. We also prove that ⌈½Δ(G)⌉ ≤ lla(G) ≤ ⌈½(Δ(G)+1)⌉ for any planar graph having Δ ≥ 9.
Keywords: list coloring, linear arboricity, list linear arboricity, planar graph 
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     author = {An, Xinhui and Wu, Baoyindureng},
     title = {The list linear arboricity of planar graphs},
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     volume = {29},
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     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a3/}
}
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An, Xinhui; Wu, Baoyindureng. The list linear arboricity of planar graphs. Discussiones Mathematicae. Graph Theory, Tome 29 (2009) no. 3, pp. 499-510. http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a3/