S ep 2 00 6 The absence of efficient dual pairs of spanning trees in planar graphs
نویسندگان
چکیده
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.
منابع مشابه
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.
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