Skip to main content
SpringerLink
Log in

Smallest maximally nonhamiltonian graphs II

  • Original Papers
  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

Bollobás posed the problem of finding the least number of edges,f(n), in a maximally nonhamiltonian graph of ordern. Clark and Entringer showedf(n)=3n/2 for all evenn≥36 andf(n)=(3n+1)/2 or (3n+3)/2 for all oddn≥55. We showf(n)=(3n+1)/2 for all oddn≥53.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bollobás, B.: Extremal Graph Theory London: Academic Press 1978

    Google Scholar 

  2. Bondy, J.A.: Variations on the hamiltonian theme. Canad. Math. Bull.,15, 57–62 (1972)

    MATH  MathSciNet  Google Scholar 

  3. Clark, L.H., Crane, R.P., Entringer, R.C., Shapiro, H.D.: On smallest maximally nonhamiltonian graphs. Congress. Numer.53, 215–220 (1986)

    MathSciNet  Google Scholar 

  4. Clark, L.H., Entringer, R.C., Shapiro, H.D.: Smallest maximally nonhamiltonian graphs II. Department of Computer Science, University of New Mexico, Technical Report CS 86-4

  5. Clark, L.H., Entringer, R.C.: Smallest maximally nonhamiltonian graphs. Periodica Mathematica Hungarica,14, 57–68 (1983)

    Article  MathSciNet  Google Scholar 

  6. Isaacs, R.: Infinite families of nontrivial trivalent graphs which are not Tait colorable. Amer. Math. Monthly,82, 221–239 (1975)

    MATH  MathSciNet  Google Scholar 

  7. Ore, O.: Arc coverings of graphs. Ann. Mat. Pura. Appl.,55, 315–321 (1961)

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, University of New Mexico, 87131, Albuquerque, NM, USA

    L. H. Clark & R. C. Entringer

  2. Department of Computer Science, University of New Mexico, 87131, Albuquerque, NM, USA

    H. D. Shapiro

Authors
  1. L. H. Clark
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. C. Entringer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. H. D. Shapiro
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Clark, L.H., Entringer, R.C. & Shapiro, H.D. Smallest maximally nonhamiltonian graphs II. Graphs and Combinatorics 8, 225–231 (1992). https://doi.org/10.1007/BF02349959

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02349959

Keywords

Search

Navigation