The Absence of Efficient Dual Pairs of Spanning Trees in Planar Graphs

A spanning tree T in a finite planar connected graph G determines a dual spanning tree T in the dual graph G such that T and T do not intersect. We show that it is not always possible to find T in G such that the diameters of T and T are both within a uniform multiplicative constant (independent of G) of the diameters of their ambient graphs.

• Type: Journal
• Year: 2006
• Where: COMBINATORICS
• Authors: T. R. Riley, William P. Thurston
• Keywords: COMBINATORICS 2006, Dual Spanning Tree, Finite Planar, Spanning Tree