Partitioning edges of a planar graph into linear forests and a matching

Abstract

AbstractWe show that the edges of any planar graph of maximum degree at most 9 can be partitioned into four linear forests and a matching. Combined with known results, this implies that the edges of any planar graph of odd maximum degree can be partitioned into linear forests and one matching. This strengthens well‐known results stating that graphs in this class have chromatic index  and linear arboricity at most .