Geodesic
Partitioning sparse plane graphs into two induced subgraphs of small degree
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 6 (2009), pp. 13-16

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A graph $G$ is said to be $(a,b)$-partitionable for positive integers $a$, $b$ if its vertices can be partitioned into subsets $V_1$ and $V_2$ such that in $G[V_1]$ any path contains at most a vertices and in $G[V_2]$ any path contains at most $b$ vertices. We prove that every planar graph of girth $8$ is $(2,2)$-partitionable.
Keywords: planar graph, coloring
Mots-clés : vertex partition. 
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     author = {O. V. Borodin and A. O. Ivanova},
     title = {Partitioning sparse plane graphs into two induced subgraphs of small degree},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {13--16},
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     year = {2009},
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O. V. Borodin; A. O. Ivanova. Partitioning sparse plane graphs into two induced subgraphs of small degree. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 6 (2009), pp. 13-16. http://geodesic.mathdoc.fr/item/SEMR_2009_6_a1/