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Covering Planar Graphs with Forests, one Having Bounded Maximum Degree

Daniel Gonçalves 1
1 ALGCO - Algorithmes, Graphes et Combinatoire
LIRMM - Laboratoire d'Informatique de Robotique et de Microélectronique de Montpellier
Abstract : We prove that every planar graph has an edge partition into three forests, one having maximum degree at most 4. This answers a conjecture of Balogh et al. (J. Combin. Theory B. 94 (2005) 147-158). We also prove that every planar graph with girth g > 5 (resp. g > 6) has an edge partition into two forests, one having maximum degree 4 (resp. 2).
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https://hal-lirmm.ccsd.cnrs.fr/lirmm-00338319
Contributor : Daniel Gonçalves <>
Submitted on : Wednesday, November 12, 2008 - 4:50:18 PM
Last modification on : Thursday, May 24, 2018 - 3:59:22 PM

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Daniel Gonçalves. Covering Planar Graphs with Forests, one Having Bounded Maximum Degree. Journal of Combinatorial Theory, Series B, Elsevier, 2009, 99 (2), pp.314-322. ⟨10.1016/j.jctb.2008.07.004⟩. ⟨lirmm-00338319⟩

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