Thresholds for Roman domination
نویسنده
چکیده
Define a Roman dominating function (RDF) of a graph G to be a function f : V (G) → {0, 1, 2} such that every u with f(u) = 0 has a neighbor v with f(v) = 2. The weight of f , w(f), is ∑ v∈V (G) f(v). The Roman domination number of G, γR(G), is the minimum weight of an RDF of G. It is easy to see that γ(G) ≤ γR(G) ≤ 2γ(G), where γ(G) is the domination number of G. In this paper, we determine probability thresholds for the events γR(G) = (1 + o(1))γ(G) and γR(G) = (2− o(1))γ(G) in the random graph model Gn,p.
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