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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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/

[1] O. V. Borodin, A. V. Kostochka, J. Nesetril, A. Raspaud, E. Sopena, “On the maximal average degree and the oriented chromatic number of a graph”, Discrete Math., 206 (1999), 77–89 | DOI | MR | Zbl

[2] O. V. Borodin, S. J. Kim, A. V. Kostochka, and D. West, “Homomorphisms of sparse graphs with large girth”, J. of Combin. Theory B, 90 (2004), 147–159 | DOI | MR | Zbl

[3] O. V. Borodin, A. O. Ivanova, A. V. Kostochka, “Orientirovannaya 5-raskraska vershin v razrezhennykh grafakh”, Diskretnyi analiz i issledovanie operatsii, 13:1 (2006), 16–32 | MR

[4] O. V. Borodin, S. G. Hartke, A. O. Ivanova, A. V. Kostochka, D. B. West, “$(5,2)$-Coloring of Sparse Graphs”, Siberian Electronic Math. Reports, 5 (2008), 417–426 | MR

[5] O. V. Borodin, A. O. Ivanova, Near-proper list vertex 2-colorings of sparse graphs, submitted

[6] A. N. Glebov, D. Zh. Zambalaeva, “Putevye razbieniya planarnykh grafov”, Sib. elektronnye mat. izvestiya, 4 (2007), 450–459 | MR | Zbl