Proximinality in geodesic spaces.
Kaewcharoen, A., Kirk, W.A. (2006)
Abstract and Applied Analysis
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Displaying similar documents to “Fixed point theorems in CAT(0) spaces and -trees.”
Proximinality in geodesic spaces.
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Products of Geodesic Graphs and the Geodetic Number of Products
Jake A. Soloff, Rommy A. Márquez, Louis M. Friedler (2015)
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Given a connected graph and a vertex x ∈ V (G), the geodesic graph Px(G) has the same vertex set as G with edges uv iff either v is on an x − u geodesic path or u is on an x − v geodesic path. A characterization is given of those graphs all of whose geodesic graphs are complete bipartite. It is also shown that the geodetic number of the Cartesian product of Km,n with itself, where m, n ≥ 4, is equal to the minimum of m, n and eight.
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Zhu, Xiaodong, Bonahon, Francis (2004)
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Ladislav Nebeský (1997)
Czechoslovak Mathematical Journal
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Publications Mathématiques de l'IHÉS
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Distance defined by spanning trees in graphs
Gary Chartrand, Ladislav Nebeský, Ping Zhang (2007)
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For a spanning tree T in a nontrivial connected graph G and for vertices u and v in G, there exists a unique u-v path u = u₀, u₁, u₂,..., uₖ = v in T. A u-v T-path in G is a u- v path u = v₀, v₁,...,vₗ = v in G that is a subsequence of the sequence u = u₀, u₁, u₂,..., uₖ = v. A u-v T-path of minimum length is a u-v T-geodesic in G. The T-distance from u to v in G is the length of a u-v T-geodesic. Let geo(G) and geo(G|T) be the set of geodesics and the set of T-geodesics respectively...