Problem of the number domatic

The problem of the number domatic is a Np-complete problem of the Graph theory.

Definition

A domatic authority of the problem of the number consists of

  • a graph G with a unit S of tops and a unit has arcs, and
  • a whole positive K lower or equal to the number of tops in G .
The problem is to determine if the Nombre domatic of G is at least K . In other words, we want to know if S can be partitioné in l \ Leq k disjoined units S_1, S_2, \ dowries, S_l such as each S_i is a Ensemble dominating for G .

Complexity

The problem of the number domatic was proven Np-complete with a reduction since the Problème 3SAT.

References

  • Michael R. Garey and David S. Johnson, Computers and Intractability: With Guide to the Theory off Np-Completeness , W.H. Freeman, 1979. ISBN 0-7167-1045-5}} A1.1: GT2, pg.190
  • Garey, Mr. R., D.S. Johnson and R.E. Tarjan, results not published.
  • Cockayne, E.J., and S.T. Hedetniemi, " Optimal domination in graphs" , Trans IEEE. Circuits and Systems CAS-22 , 855-857.

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