Article ID Journal Published Year Pages File Type
4657145 Journal of Combinatorial Theory, Series B 2009 9 Pages PDF
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, Pluhár and Yu [J. Balogh, M. Kochol, A. Pluhár, 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).

Related Topics
Physical Sciences and Engineering Mathematics Discrete Mathematics and Combinatorics