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Combinatorica

, Volume 6, Issue 3, pp 269–274 | Cite as

Contractible edges in triangle-free graphs

  • Yoshimi Egawa
  • Hikoe Enomoto
  • Akira Saito
Article

Abstract

An edge of a graph is calledk-contractible if the contraction of the edge results in ak-connected graph. Thomassen [5] proved that everyk-connected graph of girth at least four has ak-contractible edge. In this paper, we study the distribution ofk-contractible edges in triangle-free graphs and show the following: Whenk≧2, everyk-connected graph of girth at least four and ordern≧3k, hasn+(3/2)k 2-3k or morek-contractible edges.

AMS subject classification (1980)

05 C 40 

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References

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    K. Ando, H. Enomoto andA. Saito, Contractible edges in 3-connected graphs,submitted.Google Scholar
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Copyright information

© Akadémiai Kiadó 1986

Authors and Affiliations

  • Yoshimi Egawa
    • 1
  • Hikoe Enomoto
    • 2
  • Akira Saito
    • 2
  1. 1.Dept. of Applied Math.Science University of TokyoTokyoJapan
  2. 2.Dept. of Information Science Faculty of ScienceUniversity of TokyoTokyoJapan

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