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A subset D of the vertex set of a graph G is a (k, p)-dominating set if every vertex v ∈ V (G) \ D is within distance k to at least p vertices in D. The parameter γ k,p (G) denotes the minimum cardinality of a (k, p)-dominating set of G. In 1994, Bean, Henning and Swart posed the conjecture that γ k,p (G) ≤ p p+k n(G) for any graph G with δ k (G) ≥ k + p −… (More)

Preface Reality provides many examples of something we call a search. Informally, we may have a goal (e.g., finding a lost key, a damaged light bulb, the shortest way to the next bus stop) and a set of possible actions to gain some information. All possible action needs some time, money, work etc., so that we want to calculate the expenses of our search… (More)

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