Girths of bipartite sextet graphs

Abstract

An explicit construction of Biggs and Hoare yields an infinite family of bipartite cubic graphs. We prove that the ordern and girthg of each of these graphs are related by log2 n<3/4·g+3/2.

This is a preview of subscription content, access via your institution.

References

  1. [1]

    N. L. Biggs,Algebraic Graph Theory, Cambridge, 1974.

  2. [2]

    N. L. Biggs andM. J. Hoare, The sextet construction for cubic graphs,Combinatorica 3 (1983), 153–165.

    MATH  MathSciNet  Google Scholar 

  3. [3]

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

  4. [4]

    D. Z. Djoković andG. L. Miller, Regular groups of automorphisms of cubic graphs,J. Combinatorial Theory (B) 29 (1980) 195–230.

    Article  Google Scholar 

  5. [5]

    P. Erdös, andH. Sachs, Reguläre Graphen gegebener Taillenweite mit minimaler Knotenzahl.Wiss. Z. Univ. Halle—Wittenberg, Math.-Nat. R. 12 (1963), 251–258.

    MATH  Google Scholar 

  6. [6]

    I. Reiner,Maximal Orders, Academic Press, 1975.

Download references

Author information

Affiliations

Authors

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Weiss, A. Girths of bipartite sextet graphs. Combinatorica 4, 241–245 (1984). https://doi.org/10.1007/BF02579225

Download citation

AMS subject classification (1980)

  • 05 C 38
  • 05 C 25
  • 05 B 25