Showing papers by "Pinar Heggernes published in 1998"
TL;DR: This work studies the computational complexity of partitioning the vertices of a graph into generalized dominating sets, parameterized by two sets of nonnegative integers σ and ρ which constrain the neighborhood N(υ) of vertices.
Abstract: We study the computational complexity of partitioning the vertices of a graph into generalized dominating sets. Generalized dominating sets are parameterized by two sets of nonnegative integers σ and ρ which constrain the neighborhood N(υ) of vertices. A set S of vertices of a graph is said to be a (σ, ρ)-set if ∀υ ∈ S : |N(υ) ∩ S| ∈ σ and ∀υ n ∈ S : |N(υ) ∩ S| ∈ ρ. The (k, σ, ρ)-partition problem asks for the existence of a partition V1, V2, ..., Vk of vertices of a given graph G such that Vi, i = 1, 2, ...,k is a (σ, ρ)-set of G. We study the computational complexity of this problem as the parameters σ, ρ and k vary.
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