Decomposing a planar graph with girth 9 into a forest and a matching
A decomposition of a graph is a partitioning of the edge set. The authors show that any planar graph of girth 9 has a decomposition such that one part is a forest and the second part is a matching. This was previously known for planar graphs of girth 11, subsequently improved to girth 10. It is an open question if any planar graph of girth 8 decomposes into a forest and a matching. This is related to results such as a planar graph of girth 6 can be decomposed into a forest and a graph with maximum degree 2, and a planar graph can be decomposed into 3 forests such that one forest has maximum degree at most 8.
scientific article; zbMATH DE number 5280763