Dynamic monopolies for interval graphs with bounded thresholds

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Dynamic monopolies for interval graphs with bounded thresholds

For a graph G and an integer-valued threshold function τ on its vertex set, a dynamic monopoly is a set of vertices of G such that iteratively adding to it vertices u of G that have at least τ(u) neighbors in it eventually yields the vertex set of G. We show that the problem of finding a dynamic monopoly of minimum order can be solved in polynomial time for interval graphs with bounded threshol...

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Let G be a graph and τ : V (G) → N ∪ {0} be an assignment of thresholds to the vertices of G. A subset of vertices D is said to be a dynamic monopoly corresponding to (G, τ) if the vertices of G can be partitioned into subsets D0,D1, . . . ,Dk such that D0 = D and for any i ∈ {0, . . . , k − 1}, each vertex v in Di+1 has at least τ(v) neighbors in D0 ∪ . . . ∪Di. Dynamic monopolies are in fact ...

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ژورنال

عنوان ژورنال: Discrete Applied Mathematics

سال: 2019

ISSN: 0166-218X

DOI: 10.1016/j.dam.2019.01.022