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- W2080405637 abstract "Let G be a connected graph of order p and S a nonempty set of vertices of G. Then the Steiner distance d(S) of S is the minimum size of a connected subgraph of G whose vertex set contains S. If n is an integer, 2≤n≤p, the Steiner n-diameter, diamn(G), of G is the maximum Steiner distance of any n-subset of vertices of G. We give a bound on diamn(G) for a graph G in terms of the order of G and the minimum degree of G. Our result implies a bound on the ordinary diameter by Erdős, Pach, Pollack and Tuza. We obtain improved bounds on diamn(G) for K3-free graphs and C4-free graphs. Moreover, we construct graphs to show that the bounds are asymptotically best possible." @default.
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- W2080405637 date "2012-08-01" @default.
- W2080405637 modified "2023-10-01" @default.
- W2080405637 title "Upper bounds on the Steiner diameter of a graph" @default.
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- W2080405637 doi "https://doi.org/10.1016/j.dam.2012.03.031" @default.
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