The list linear arboricity of planar graphs
Xinhui An ; Baoyindureng Wu
Discussiones Mathematicae Graph Theory, Tome 29 (2009), p. 499-510 / Harvested from The Polish Digital Mathematics Library
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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.

Publié le : 2009-01-01
EUDML-ID : urn:eudml:doc:271000 
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Xinhui An; Baoyindureng Wu. The list linear arboricity of planar graphs. Discussiones Mathematicae Graph Theory, Tome 29 (2009) pp. 499-510. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1460/

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