On spaces extremal for the Gomory-Hu inequality

DOI10.1134/S2070046615020053zbMath1343.05072arXiv1412.1979OpenAlexW1662909231MaRDI QIDQ498716

Aleksey A. Dovgoshey, Hanns-Martin Teichert, Evgenii A. Petrov

Publication date: 29 September 2015

Published in: \(p\)-Adic Numbers, Ultrametric Analysis, and Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1412.1979

zbMATH Keywords

binary treeweighted graphfinite ultrametric space\(\epsilon\)-isometryballpreserving mappingweak similarity

Mathematics Subject Classification ID

Deterministic network models in operations research (90B10) Topological spaces with richer structures (54E99) Enumeration in graph theory (05C30) Paths and cycles (05C38) Eulerian and Hamiltonian graphs (05C45) Semimetric spaces (54E25) Signed and weighted graphs (05C22)

Related Items (14)

Minimum spanning paths and Hausdorff distance in finite ultrametric spaces ⋮ How rigid the finite ultrametric spaces can be? ⋮ Labeled trees generating complete, compact, and discrete ultrametric spaces ⋮ Uniqueness of best proximity pairs and rigidity of semimetric spaces ⋮ Bipartite graphs and best proximity pairs ⋮ Hereditary properties of finite ultrametric spaces ⋮ On ultrametric-preserving functions ⋮ Combinatorial properties of ultrametrics and generalized ultrametrics ⋮ Finite ultrametric balls ⋮ The range of ultrametrics, compactness, and separability ⋮ On some extremal properties of finite ultrametric spaces ⋮ Ultrametric preserving functions and weak similarities of ultrametric spaces ⋮ From isomorphic rooted trees to isometric ultrametric spaces ⋮ Properties and morphisms of finite ultrametric spaces and their representing trees

Uses Software

• OEIS

Cites Work

• Characterizing (quasi-)ultrametric finite spaces in terms of (directed) graphs
• On the Gomory-Hu inequality
• Trees and ultrametric spaces: A categorical equivalence
• Exact enumeration of cherries and pitchforks in ranked trees under the coalescent model
• Weak similarities of metric and semimetric spaces
• Subdominant pseudoultrametric on graphs
• Multi-Terminal Network Flows
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