Limited dominating broadcasts were proposed as a variant of dominating broadcasts, where the broadcast function is upper bounded by a constant k . The minimum cost of such a dominating broadcast is the k -broadcast dominating number. We present a uni ed upper bound on this parameter for any value of k in terms of both k and the order of the graph. For the speci c case of the 2-broadcast dominating number, we show that this bound is tight for graphs as large as desired. We also study the family of caterpillars, providing a smaller upper bound, which is attained by a set of such graphs with unbounded order.Preprin
