Partitioning a triangle-free planar graph into a forest and a forest of bounded degree

François Dross 1 Mickaël Montassier 1 Alexandre Pinlou 1
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We prove that every triangle-free planar graph can have its set of vertices partitioned into two sets, one inducing a forest and the other a forest with maximum degree at most 5. We also show that if for some d, there is a triangle-free planar graph that cannot be partitioned into two sets, one inducing a forest and the other a forest with maximum degree at most d, then it is an NP-complete problem to decide if a triangle-free planar graph admits such a partition.
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-01233461
Contributor : Alexandre Pinlou <>
Submitted on : Wednesday, November 25, 2015 - 11:28:57 AM
Last modification on : Thursday, May 24, 2018 - 3:59:22 PM

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François Dross, Mickaël Montassier, Alexandre Pinlou. Partitioning a triangle-free planar graph into a forest and a forest of bounded degree. EuroComb: European Conference on Combinatorics, Graph Theory and Applications, Aug 2015, Bergen, Norway. pp.269-275, ⟨10.1016/j.endm.2015.06.037⟩. ⟨lirmm-01233461⟩

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