, Volume 16, Issue 4, pp 555–566 | Cite as

The gallai-younger conjecture for planar graphs

  • B. A. Reed
  • F. B. Shepherd


Younger conjectured that for everyk there is ag(k) such that any digraphG withoutk vertex disjoint cycles contains a setX of at mostg(k) vertices such thatG−X has no directed cycles. Gallai had previously conjectured this result fork=1. We prove this conjecture for planar digraphs. Specifically, we show that ifG is a planar digraph withoutk vertex disjoint directed cycles, thenG contains a set of at mostO(klog(k)log(log(k))) vertices whose removal leaves an acyclic digraph. The work also suggests a conjecture concerning an extension of Vizing's Theorem for planar graphs.

Mathematics Subject Classification (1991)

05 C 75 05 C 70 90 C 10 90 C 27 


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Copyright information

© Akadémiai Kiadó 1996

Authors and Affiliations

  • B. A. Reed
    • 1
  • F. B. Shepherd
    • 2
  1. 1.CNRSUniversité Paris VIParisFrance
  2. 2.Centre for Discrete and Applicable MathematicsLSELondonU. K.

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