论文信息 - Covering planar graphs with forests, one having a bounded maximum degree

Covering planar graphs with forests, one having a bounded maximum degree

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).

D. Gonçalves | D. Gonçalves

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