Compatible decompositions and block realizations of finite metrics

DOI10.1016/j.ejc.2007.10.003zbMath1179.05029OpenAlexW2167684499MaRDI QIDQ942132

Katharina T. Huber, Andreas W. M. Dress, Vincent L. Moulton, Jack H. Koolen

Publication date: 4 September 2008

Published in: European Journal of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.ejc.2007.10.003

zbMATH Keywords

phylogenetic treecompatible decompositioncompatible split systemsplit metric

Mathematics Subject Classification ID

Trees (05C05) Metric spaces, metrizability (54E35)

Related Items (9)

Block realizations of finite metrics and the tight-span construction. I: The embedding theorem ⋮ The polytopal structure of the tight-span of a totally split-decomposable metric ⋮ Obtaining splits from cut sets of tight spans ⋮ Cut points in metric spaces ⋮ Compatible decompositions and block realizations of finite metrics ⋮ Optimal realizations and the block decomposition of a finite metric space ⋮ A graph-theoretical invariant of topological spaces ⋮ Barriers in metric spaces ⋮ An algorithm for computing cutpoints in finite metric spaces

Cites Work

• On optimal embeddings of metrics in graphs
• Gated sets in metric spaces
• Compatible decompositions and block realizations of finite metrics
• Trees, tight extensions of metric spaces, and the cohomological dimension of certain groups: A note on combinatorial properties of metric spaces
• Distance-hereditary graphs
• On optimal realizations of finite metric spaces by graphs
• A canonical decomposition theory for metrics on a finite set
• On metric properties of certain clique graphs
• Trees, taxonomy, and strongly compatible multi-state characters
• Hereditarily optimal realizations of consistent metrics
• Six theorems about injective metric spaces
• The Complexity of Metric Realization
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