Abstract:Let G be a connected graph with the usual shortest-path metric d. The graph G is δ-hyperbolic provided for any vertices x, y, u, v in it, the two larger of the three sums d(u, v)+ d(x, y), d(u, x)+ d(v, y) and d(u, y) + d(v, x) differ by at most 2δ. The graph G is k-chordal provided it has no induced cycle of length greater than k. Brinkmann, Koolen and Moulton find that every 3-chordal graph is 1-hyperbolic and is not 1 2 -hyperbolic if and only if it contains one of two special graphs as an isometric subgrap… Show more
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