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The binding number of a graph and its triangle

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Abstract

In this paper we prove the following conjecture of Woodall[1]: if bind (G)≥3/2, thenG contains a triangle. Moreover we also prove that if bind (G)≥3/2, then each vertex is contained in a 4-cycle, each edge is contained in a 5-cycle whenV(G)≥11, and there exists a 6-cycle inG.

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References

  1. [1]

    Woodall, D. R., The Binding Number of a Graph and Its Anderson Number,J. of Combinatorial Theory (B),15 (1973), 225–255.

  2. [2]

    Kare, V. G. and Mohanty, S. P., Binding Number, Cycles and Complete Graphs, Lec. Notes in Math. 885, Combinatorics and Graph Theory, Proceeding Calcutta, Springer-Verlag, Berlin, Heidelberg New York, 1980, 290–296.

  3. [3]

    Bollobas, B., Extremal Graph Theory, Academic Press, 1978.

  4. [4]

    Deng Xiaotie, The Binding Number of a Graph and Its Hamiltonian Connectivity (to appear).

  5. [5]

    Bondy, J. A. and Murty, U. S. R., Graph Theory with Applications, MacMillan, London, 1976.

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Ronghua, S. The binding number of a graph and its triangle. Acta Mathematicae Applicatae Sinica 2, 79–86 (1985). https://doi.org/10.1007/BF01666521

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Keywords

  • Math Application
  • Binding Number