Combinatorica

, Volume 22, Issue 3, pp 335–343

A Tree Version of Kőnig's Theorem

  • Ron Aharoni
  • Eli Berger
  • Ran Ziv
Original Paper

Kőnig's theorem states that the covering number and the matching number of a bipartite graph are equal. We prove a generalization, in which the point in one fixed side of the graph of each edge is replaced by a subtree of a given tree. The proof uses a recent extension of Hall's theorem to families of hypergraphs, by the first author and P. Haxell [2]. As an application we prove a special case (that of chordal graphs) of a conjecture of B. Reed.

AMS Subject Classification (2000) Classes:  05C70 

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Copyright information

© János Bolyai Mathematical Society, 2002

Authors and Affiliations

  • Ron Aharoni
    • 1
  • Eli Berger
    • 2
  • Ran Ziv
    • 3
  1. 1.Department of Mathematics, Technion; Haifa Israel 32000; E-mail: ra@tx.technion.ac.ilIL
  2. 2.Department of Mathematics, Technion; Haifa Israel 32000; E-mail: eberger@princeton.eduIL
  3. 3.Department of Computer Science, Tel-Hai College; Upper Galilee, Israel 12210; E-mail: ranziv@telhai.ac.ilIL

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