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The absence of efficient dual pairs of spanning trees in planar graphs

T. R. Riley·W. P. Thurston
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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.

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T. R. Riley, W. P. Thurston. 2006-09-07. The absence of efficient dual pairs of spanning trees in planar graphs. https://arxiv.org/abs/math/0511493

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