Hamiltonicity of planar cubic multigraphs

Abstract

Hamiltonicity of connected cubic planar general graphs G is characterized in terms of partitioning any dual graph G ∗ into two trees. Thus tree–tree triangulations become involved. The related Stein theorem is corrected and extended. Moreover, it follows that a maximal planar graph G can be partitioned into two forests if and only if G can be partitioned into two trees.