Abstract:Slimness of a graph measures the local deviation of its metric from a tree metric. In a graph G = (V, E), a geodesic triangle (x, y, z) with x, y, z ∈ V is the union P (x, y) ∪ P (x, z) ∪ P (y, z) of three shortest paths connecting these vertices. A geodesic triangle (x, y, z) is called δ-slim if for any vertex u ∈ V on any side P (x, y) the distance from u to P (x, z) ∪ P (y, z) is at most δ, i.e. each path is contained in the union of the δ-neighborhoods of two others. A graph G is called δ-slim, if all geod… Show more
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