Skip to main content
SpringerLink
Log in

Spanning eulerian subgraphs of bounded degree in triangulations

  • Published:
Graphs and Combinatorics Aims and scope Submit manuscript

Abstract

We show that every triangulation of a disk or an annulus has a spanning Eulerian subgraph with maximum degree eight.

Since every triangulation in the projective plane, the torus and the Klein bottle has a spanning subgraph which triangulates an annulus, this implies that all triangulations in the projective plane, the torus and the Klein bottle have spanning Eulerian subgraphs with maximum degree at most eight.

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. Barnette, D.W.: Trees in polyhedral graphs. Canad. J. Math.18, 731–736 (1966)

    MATH  MathSciNet  Google Scholar 

  2. Brunet, R., Ellingham, M.N., Gao, ?., Metzlar, ?., Richter, R.B.: Spanning planar subgraphs of graphs in the torus and Klein bottle. (submitted)

  3. Brunet, R., Richter, R.B.: Hamiltonicity of 5-connected toroidal triangulations. (submitted)

  4. Ellingham, M.N., Gao, ?.: Spanning trees in locally planar triangulations. J. Comb. Theory, Ser. B (to be published)

  5. Fiedler, J., Huneke, J.P. Richter, R.B., Robertson, N.: Computing the orientable genus of projective graphs, (submitted)

  6. Gao, ?., Richter, R.B.: 2-walks.in circuit graphs. J. Comb. Theory, Ser. B (to be published)

  7. Jackson, B., Wormald, N.C.: k-walks of graphs. Australasian J. of Combinatorics2, 135–146 (1990)

    MATH  MathSciNet  Google Scholar 

  8. Richmond, L.B., Robinson, R.W., Wormald, N.C.: On Hamilton cycles in 3-connected cubic maps. In “Cycles in Graphs” (B. Alspach and CD. Godsil, eds.) Annals of Discrete Mathematics27, 141–150 (1985)

    MathSciNet  Google Scholar 

  9. Thomas, R., Yu, X.: Planar and projective-planar Hamiltonian graphs. J. Comb. Theory, Ser. B (to be published)

  10. Thomas, R., Yu, X.: Toroidal Hamiltonian graphs (in preparation)

  11. Thomassen, C.: A theorem on paths in planar graphs. J. Graph Theory7, 169–176 (1983)

    Article  MATH  MathSciNet  Google Scholar 

  12. Thomassen, C.: Trees in triangulations. J. Comb. Theory, Ser. B (to be published)

  13. Tutte, W.T.: A theorem on planar graphs. Trans. Amer. Math. Soc.82, 99–116 (1956)

    Article  MATH  MathSciNet  Google Scholar 

  14. Tutte, W.T.: Bridges and Hamiltonian circuits in planar graphs. Aeq. Math.15, 1–33 (1977)

    Article  MATH  MathSciNet  Google Scholar 

  15. Whitney, H.: A theorem on graphs. Ann. of Math.32, 378–390 (1931)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept of Mathematics and Statistics, Carleton University Ottawa, S 5B6, Canada

    Zhicheng Gao

  2. Department of Mathematics, University of Melbourne, VIC 3052, Parkville, Australia

    Nicholas C. Wormald

Authors
  1. Zhicheng Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nicholas C. Wormald
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Research supported by the Australian Research Council

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gao, Z., Wormald, N.C. Spanning eulerian subgraphs of bounded degree in triangulations. Graphs and Combinatorics 10, 123–131 (1994). https://doi.org/10.1007/BF02986656

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02986656

Keywords

Search

Navigation