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Contractible edges in triangle-free graphs

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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.

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References

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Authors and Affiliations

  1. Dept. of Applied Math., Science University of Tokyo, Shinjuku-ku, 162, Tokyo, Japan

    Yoshimi Egawa

  2. Dept. of Information Science Faculty of Science, University of Tokyo, Hongo, Bunkyo-ku, 113, Tokyo, Japan

    Hikoe Enomoto & Akira Saito

Authors
  1. Yoshimi Egawa
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  2. Hikoe Enomoto
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  3. Akira Saito
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Egawa, Y., Enomoto, H. & Saito, A. Contractible edges in triangle-free graphs. Combinatorica 6, 269–274 (1986). https://doi.org/10.1007/BF02579387

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  • DOI: https://doi.org/10.1007/BF02579387

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