Covering planar graphs with forests

Authors:
József Balogh;Martin Kochol;András Pluhár;Xingxing Yu
Affiliations:
Department of Mathematical Sciences, The Ohio State University, Columbus, OH;MÚ SAV, Štefánikova 49, 814 73 Bratislava 1, Slovakia;University of Szeged, Department of Computer Science, Árpád tér 2, Szeged, H-6720, Hungary;School of Mathematics, Georgia Institute of Technology, Atlanta, GA and Center for Combinatorics, LPMC, Nankai University, Tianjin 300071, PR China
Venue:
Journal of Combinatorial Theory Series B
Year:
2005

Citing 1
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Abstract

We study the problem of covering graphs with trees and a graph of bounded maximum degree. By a classical theorem of Nash-Williams, every planar graph can be covered by three trees. We show that every planar graph can be covered by two trees and a forest, and the maximum degree of the forest is at most 8. Stronger results are obtained for some special classes of planar graphs.