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In a classical 1986 paper by Erdös, Saks and Saós every graph of radius r has an induced path of order at least 2r − 1. This result implies that the independence number of such graphs is at least r. In this paper, we use a result of S. Fajtlowicz about radius-critical graphs to characterize graphs where the independence number is equal to the radius, for all possible values of the radius except 2,...
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