Abstract: Using the weight transfer method, we studied the vertex-partition problem for planar graphs without 4,6-cycles, and obtained that the vertex set of a graph G without adjacent 5-cycles could be partitioned into two subsets, so that the derived subgraph of each subset was a forest with maximum degree at most 3. This  improved the conclusion about the existence of  (F₅,F₅)-partition of planar graphs without 4,6-cycles.

Key words: forest partition, weight transfer, vertex coloring, planar graph