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The problem of finding a minimum k -basis of graph G is that of selecting as small a set B of vertices as possible such that every vertex of G is at distance k or less from some vertex in B . Cockayne, Goodman, and Hedetniemi previously developed a linear algorithm to find a minimum 1-basis (a minimum dominating set) when G is a tree. In this paper the k -basis problem is placed in a more general setting, and a linear algorithm is presented that solves the problem for any forest.
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Peter J. Slater (1976) studied this question.
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