k-optimal Partitions of a Directed Graph

  title={k-optimal Partitions of a Directed Graph},
  author={Claude Berge},
  journal={Eur. J. Comb.},
A partition M is k-optimal if M minimizes BdM). For instance, if G has a Hamiltonian path J.Lo, then M = W.o} is a k -optimal partition. So the k -optimal partitions extend in some sense the concept of Hamiltonian paths. The theorem of Greene and Kleitman [10], which extends the Dilworth theorem [5], shows an important property of k-optimal partitions for the graph of a partially ordered set (in [1, 5], the k-optimal partitions are called "k-saturated"). This paper shows that similar properties… CONTINUE READING

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