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# k-optimal Partitions of a Directed Graph

@article{Berge1982koptimalPO, title={k-optimal Partitions of a Directed Graph}, author={Claude Berge}, journal={Eur. J. Comb.}, year={1982}, volume={3}, pages={97-101} }

- Published 1982 in Eur. J. Comb.
DOI:10.1016/S0195-6698(82)80022-X

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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