2012/11/11 by Evgeniy Petrov, Oleksiy Dovgoshey, Petrov, E. +1
Mathematics · #37E25 #54E35 #Advanced Banach Space Theory #FOS: Mathematics #Fixed Point Theorems Analysis #Geometric Analysis and Curvature Flows #Metric Geometry (math.MG)
paper · pdf · doi:10.48550/arxiv.1211.2389
openalex publication_date 2012/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It was proved by Gomori and Hu in 1961 that for every finite nonempty ultrametric space (X,d) the following inequality |\Sp(X)|\leqslant |X|-1 holds with \Sp(X)=\d(x,y):x,y ∈ X, x≠ y\. We characterize the spaces X, for which the equality in this inequality is attained by the structural properties of some graphs and show that the set of isometric types of such X is dense in the Gromov-Hausdorff space of the compact ultrametric spaces.