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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Electronic Notes in Discrete Mathematics, Elsevier, 2015, The Eight European Conference on Combinatorics, Graph Theory and Applications, EuroComb 2015, 49, pp.269-275. 〈10.1016/j.endm.2015.06.037〉
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-01233461
Contributeur : Alexandre Pinlou <>
Soumis le : mercredi 25 novembre 2015 - 11:28:57
Dernière modification le : jeudi 11 janvier 2018 - 06:26:13

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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. Electronic Notes in Discrete Mathematics, Elsevier, 2015, The Eight European Conference on Combinatorics, Graph Theory and Applications, EuroComb 2015, 49, pp.269-275. 〈10.1016/j.endm.2015.06.037〉. 〈lirmm-01233461〉

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