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

1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : An $({\cal F},{\cal F}_d)$-partition of a graph is a vertex-partition into two sets $F$ and $F_d$ such that the graph induced by $F$ is a forest and the one induced by $F_d$ is a forest with maximum degree at most $d$. We prove that every triangle-free planar graph admits an $({\cal F},{\cal F}_5)$-partition. Moreover we show that if for some integer $d$ there exists a triangle-free planar graph that does not admit an $({\cal F},{\cal F}_d)$-partition, then it is an NP-complete problem to decide whether a triangle-free planar graph admits such a partition.
Document type :
Journal articles

https://hal-lirmm.ccsd.cnrs.fr/lirmm-01430784
Contributor : Mickael Montassier <>
Submitted on : Tuesday, January 10, 2017 - 11:40:37 AM
Last modification on : Sunday, December 15, 2019 - 3:18:02 PM

### Citation

François Dross, Mickaël Montassier, Alexandre Pinlou. Partitioning a triangle-free planar graph into a forest and a forest of bounded degree. European Journal of Combinatorics, Elsevier, 2017, 66, pp.81-94. ⟨10.1016/j.ejc.2017.06.014⟩. ⟨lirmm-01430784⟩

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