Contractible edges in triangle-free graphs

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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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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AMS subject classification (1980)

  • 05 C 40