For an unweighted graph G=(V,E), we say G'=(V,E') is a subgraph if E' is contained in E. Also G''=(V'',E'',omega) is a Steiner graph if V is contained in V'', and for any pair of vertices u,w in V, the distance between them in G'' is at least the distance between them in G. In this paper we introduce the notion of distance preserver. A subgraph (resp., Steiner graph) G' of a graph G is a subgraph (resp., Steiner) D-preserver of G if for every pair of vertices u,w in V whose distance in G is at least D, their distance in G' is the same as their distance in G. We give upper and lower bounds on the number of edges required for D-preservers of various flavors.
By: Bela Bollobas, Don Coppersmith, Michael Elkin
Published in: RC22578 in 2002
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