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Combinatorial theorems about embedding trees on the real line
2011
Journal of Graph Theory
We consider the combinatorial problem of embedding the metric defined by an unweighted graph into the real line, so as to minimize the distortion of the embedding. This problem is inspired by connections to Banach space theory and to computer science. After establishing a framework in which to study line embeddings, we focus on metrics defined by three specific families of trees: complete binary trees, fans, and combs. We construct asymptotically optimal (i.e., distortion-minimizing) line
doi:10.1002/jgt.20608
fatcat:vtkcxehxerggrnp2jf4lgajotq