# The list linear arboricity of planar graphs

Discussiones Mathematicae Graph Theory (2009)

- Volume: 29, Issue: 3, page 499-510
- ISSN: 2083-5892

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topXinhui An, and Baoyindureng Wu. "The list linear arboricity of planar graphs." Discussiones Mathematicae Graph Theory 29.3 (2009): 499-510. <http://eudml.org/doc/271000>.

@article{XinhuiAn2009,

abstract = {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.},

author = {Xinhui An, Baoyindureng Wu},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {list coloring; linear arboricity; list linear arboricity; planar graph},

language = {eng},

number = {3},

pages = {499-510},

title = {The list linear arboricity of planar graphs},

url = {http://eudml.org/doc/271000},

volume = {29},

year = {2009},

}

TY - JOUR

AU - Xinhui An

AU - Baoyindureng Wu

TI - The list linear arboricity of planar graphs

JO - Discussiones Mathematicae Graph Theory

PY - 2009

VL - 29

IS - 3

SP - 499

EP - 510

AB - 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.

LA - eng

KW - list coloring; linear arboricity; list linear arboricity; planar graph

UR - http://eudml.org/doc/271000

ER -

## References

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