Covering planar graphs with forests, one having bounded maximum degree

Authors:
D. Gonçalves
Affiliations:
LIRMM UMR 5506, CNRS, Univ. Montpellier 2, 161 rue Ada, 34 392 Montpellier Cedex 5, France
Venue:
Journal of Combinatorial Theory Series B
Year:
2009

Citing 3
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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, Kochol, Pluhar and Yu [J. Balogh, M. Kochol, A. Pluhar, X. Yu, Covering planar graphs with forests, J. Combin. Theory Ser. B. 94 (2005) 147-158]. We also prove that every planar graph with girth g=6 (resp. g=7) has an edge partition into two forests, one having maximum degree at most 4 (resp. 2).