Bibliography on domination in graphs and some basic definitions of domination parameters
Discrete Mathematics - Topics on domination
Selected papers of the 14th British conference on Combinatorial conference
Algorithms for Vertex Partitioning Problems on Partial k-Trees
SIAM Journal on Discrete Mathematics
Complexity of domination-type problems in graphs
Nordic Journal of Computing
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Coloring powers of planar graphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Generalized H-Coloring of Graphs
ISAAC '00 Proceedings of the 11th International Conference on Algorithms and Computation
The Chromatic Number of Graph Powers
Combinatorics, Probability and Computing
A complete complexity classification of the role assignment problem
Theoretical Computer Science - Graph colorings
An improved exact algorithm for the domatic number problem
Information Processing Letters
Fall colouring of bipartite graphs and cartesian products of graphs
Discrete Applied Mathematics
The computational complexity of the role assignment problem
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Computational complexity of generalized domination: a complete dichotomy for chordal graphs
WG'07 Proceedings of the 33rd international conference on Graph-theoretic concepts in computer science
ESA'07 Proceedings of the 15th annual European conference on Algorithms
Generalized domination in degenerate graphs: a complete dichotomy of computational complexity
TAMC'08 Proceedings of the 5th international conference on Theory and applications of models of computation
Parameterized complexity of generalized domination problems
Discrete Applied Mathematics
Branch and recharge: exact algorithms for generalized domination
WADS'07 Proceedings of the 10th international conference on Algorithms and Data Structures
Fast dynamic programming for locally checkable vertex subset and vertex partitioning problems
Theoretical Computer Science
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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.