Abstract
Two plane geometric graphs are said to be compatible when their union is a plane geometric graph. Let S be a set of n points in the Euclidean plane in general position and let T be any given plane geometric spanning tree of S. In this work, we study the problem of finding a second plane geometric tree T′ spanning S, such that T′ is compatible with T and shares the minimum number of edges with T. We prove that there is always a compatible plane geometric tree T′ having at most (n−3)/4 edges in common with T, and that for some plane geometric trees T, any plane tree T′ spanning S, compatible with T, has at least (n−2)/5 edges in common with T.
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