Decomposing a planar graph with girth at least 8 into a forest and a matching

AbstractW. He et al. showed that a planar graph of girth at least 11 can be decomposed into a forest and a matching. A. Bass et al. proved the same statement for planar graphs of girth at least 10. Recently, O.V. Borodin et al. improved the bound on the girth to 9. In this paper, we further improve the bound on the girth to 8. This bound is the best possible in the sense that there are planar graphs with girth 7 that cannot be decomposed into a forest and a matching