A New Proof of Berge’s Strong Path Partition Conjecture for Acyclic Digraphs
نویسنده
چکیده
Berge’s elegant strong path partition conjecture from 1982 extends the Greene-Kleitman Theorem and Dilworth’s Theorem for all digraphs. The conjecture is known to be true for all digraphs for k = 1 by the Gallai-Milgram Theorem, and for k > 1 only for acyclic digraphs. We present a simple algorithmic proof for k = 1 which naturally extends to a new algorithmic proof for acyclic digraphs for all k ≥ 1. We conclude with some ideas for extending the algorithm for all digraphs.
منابع مشابه
Proof of Berge's strong path partition conjecture for k=2
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 conjec...
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