Decomposing a planar graph with girth 9 into a forest and a matching

Authors:
Oleg V. Borodin;Alexandr V. Kostochka;Naeem N. Sheikh;Gexin Yu
Affiliations:
Sobolev Institute of Mathematics, Novosibirsk 630090, Russia;Department of Mathematics, University of Illinois, Urbana, IL 61801, USA and Sobolev Institute of Mathematics, Novosibirsk 630090, Russia;Department of Mathematics, University of Illinois, Urbana, IL 61801, USA;Department of Mathematics, Vanderbilt University, Nashville, TN 37240, USA
Venue:
European Journal of Combinatorics
Year:
2008

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Abstract

W. He et al. showed that a planar graph of girth 11 can be decomposed into a forest and a matching. D. Kleitman et al. proved the same statement for planar graphs of girth 10. We further improve the bound on girth to 9.