Partitions of graphs into one or two independent sets and cliques
Discrete Mathematics
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A distributed strict strong coloring algorithm for broadcast applications in ad hoc networks
NOTERE '08 Proceedings of the 8th international conference on New technologies in distributed systems
A graph coloring based service discovery in ad hoc networks
Proceedings of the 3rd workshop on Agent-oriented software engineering challenges for ubiquitous and pervasive computing
A strict strong coloring of trees
Information Processing Letters
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A proper k-coloring C1, C2,...,Ck of a graph G is called strong if, for every vertex u ∈ V(G), there exists an index i ∈ {1, 2,...,k} such that u is adjacent to every vertex of Ci. We consider classes SCOLOR(k) of strongly k-colorable graphs and show that the recognition problem of SCOLOR(k) is NP-complete for every k ≥ 4, but it is polynomial-time solvable for k = 3. We give a characterization of SCOLOR(3) in terms of forbidden induced subgraphs. Finally, we solve the problem of uniqueness of a strong 3-coloring.