Decompositions of quadrangle-free planar graphs
Oleg Veniaminovich Borodin, Anna O. Ivanova, Alexander V. Kostochka, Naeem Nisar Sheikh · Discussiones Mathematicae Graph Theory · 2009
W. He et al. showed that a planar graph not containing 4-cycles can be decomposed into a forest and a graph with maximum degree at most 7. This degree restriction was improved to 6 by Borodin et al. We further lower this bound to 5 and show that it cannot be improved to 3.