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

Voir la notice de l'article provenant de la source Library of Science

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 
@article{DMGT_2009_29_3_a3,
     author = {An, Xinhui and Wu, Baoyindureng},
     title = {The list linear arboricity of planar graphs},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {499--510},
     publisher = {mathdoc},
     volume = {29},
     number = {3},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a3/}
}
TY  - JOUR
AU  - An, Xinhui
AU  - Wu, Baoyindureng
TI  - The list linear arboricity of planar graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2009
SP  - 499
EP  - 510
VL  - 29
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a3/
LA  - en
ID  - DMGT_2009_29_3_a3
ER  - 
%0 Journal Article
%A An, Xinhui
%A Wu, Baoyindureng
%T The list linear arboricity of planar graphs
%J Discussiones Mathematicae. Graph Theory
%D 2009
%P 499-510
%V 29
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2009_29_3_a3/
%G en
%F DMGT_2009_29_3_a3
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/

[1] J. Akiyama, G. Exoo and F. Harary, Covering and packing in graphs III: Cyclic and acyclic invariants, Math. Slovaca 30 (1980) 405-417.

[2] J. Akiyama, G. Exoo and F. Harary, Covering and packing in graphs IV: Linear arboricity, Networks 11 (1981) 69-72, doi: 10.1002/net.3230110108.

[3] X. An and B. Wu, List linear arboricity of series-parallel graphs, submitted.

[4] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications (American Elsevier, New York, Macmillan, London, 1976).

[5] O.V. Borodin, On the total colouring of planar graphs, J. Reine Angew. Math. 394 (1989) 180-185, doi: 10.1515/crll.1989.394.180.

[6] H. Enomoto and B. Péroche, The linear arboricity of some regular graphs, J. Graph Theory 8 (1984) 309-324, doi: 10.1002/jgt.3190080211.

[7] F. Guldan, The linear arboricity of 10 regular graphs, Math. Slovaca 36 (1986) 225-228.

[8] F. Harary, Covering and packing in graphs I, Ann. N.Y. Acad. Sci. 175 (1970) 198-205, doi: 10.1111/j.1749-6632.1970.tb56470.x.

[9] J.L. Wu, On the linear arboricity of planar graphs, J. Graph Theory 31 (1999) 129-134, doi: 10.1002/(SICI)1097-0118(199906)31:2129::AID-JGT5>3.0.CO;2-A

[10] J.L. Wu, The linear arboricity of series-parallel graphs, Graphs Combin. 16 (2000) 367-372, doi: 10.1007/s373-000-8299-9.

[11] J.L. Wu, J.F. Hou and G.Z. Liu, The linear arboricity of planar graphs with no short cycles, Theoretical Computer Science 381 (2007) 230-233, doi: 10.1016/j.tcs.2007.05.003.

[12] J.L. Wu and Y.W. Wu, The linear arboricity of planar graphs of maximum degree seven is four, J. Graph Theory 58 (2008) 210-220, doi: 10.1002/jgt.20305.