Proof of Berge's strong path partition conjecture for k = 2

Eli Berger, Irith Ben-Arroyo Hartman

Research output: Contribution to journalArticlepeer-review


Berge's strong path partition conjecture from 1982 generalizes and extends Dilworth's theorem and the Greene-Kleitman theorem which are well known for partially ordered sets. The conjecture is known to be true for all digraphs only for k = 1 (by the Gallai-Milgram theorem) and for k ≥ λ (where λ is the cardinality of the longest path in the graph). The attempts made, so far, to prove the conjecture for other values of k have yielded proofs for acyclic digraphs, but not for general digraphs. In this paper, we prove the conjecture for k = 2 for all digraphs. The proof is constructive and it extends the proof for k = 1.

Original languageEnglish
Pages (from-to)179-192
Number of pages14
JournalEuropean Journal of Combinatorics
Issue number1
StatePublished - Jan 2008

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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