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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{SEMR_2008_5_a16,
     author = {O. V. Borodin and A. O. Ivanova},
     title = {List $2$-arboricity of planar graphs with no triangles at distance less than two},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {211--214},
     publisher = {mathdoc},
     volume = {5},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2008_5_a16/}
}
TY  - JOUR
AU  - O. V. Borodin
AU  - A. O. Ivanova
TI  - List $2$-arboricity of planar graphs with no triangles at distance less than two
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2008
SP  - 211
EP  - 214
VL  - 5
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2008_5_a16/
LA  - en
ID  - SEMR_2008_5_a16
ER  - 
%0 Journal Article
%A O. V. Borodin
%A A. O. Ivanova
%T List $2$-arboricity of planar graphs with no triangles at distance less than two
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2008
%P 211-214
%V 5
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2008_5_a16/
%G en
%F SEMR_2008_5_a16
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/