A Structural Property of Trees with an Application to Vertex-Arboricity

الملخص EN

We provide a structural property of trees, which is applied to show that if a plane graph G contains two edge-disjoint spanning trees, then its dual graph G⁎ has the vertex-arboricity at most 2.

We also show that every maximal plane graph of order at least 4 contains two edge-disjoint spanning trees.