The absence of efficient dual pairs of spanning trees in planar graphs
Combinatorics
2007-05-23 v2 Group Theory
Abstract
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.
Cite
@article{arxiv.math/0511493,
title = {The absence of efficient dual pairs of spanning trees in planar graphs},
author = {T. R. Riley and W. P. Thurston},
journal= {arXiv preprint arXiv:math/0511493},
year = {2007}
}
Comments
7 pages, 3 figures