Geodesic
The absence of efficient dual pairs of spanning trees in planar graphs
The electronic journal of combinatorics, Tome 13 (2006)

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Zbl arXiv EuDML
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.
DOI : 10.37236/1151
Classification : 05C10, 05C12, 20F06, 57M15
Mots-clés : diameters 
T. R. Riley; W. P. Thurston. The absence of efficient dual pairs of spanning trees in planar graphs. The electronic journal of combinatorics, Tome 13 (2006). doi: 10.37236/1151
@article{10_37236_1151,
     author = {T. R. Riley and W. P. Thurston},
     title = {The absence of efficient dual pairs of spanning trees in planar graphs},
     journal = {The electronic journal of combinatorics},
     year = {2006},
     volume = {13},
     doi = {10.37236/1151},
     zbl = {1097.05015},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/1151/}
}
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