Skip to main content
Log in

Amalgams of Cubic Bipartite Graphs

  • Published:
Designs, Codes and Cryptography Aims and scope Submit manuscript

Abstract

The amalgamation technique has been introduced for groups by Higman et al. [8] and Goldschmidt [7] and developed on geometries by Kegel and Schleiermacher [9]. We define a “graph amalgam” to point out a different approach to certain classes of cubic bipartite graphs. Furthermore, we find relations between graph amalgams, 3-bridges and star-products of cubic bipartite graphs.

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

Access this article

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. J. Di Paola and H. Gropp, Symmetric configurations without blocking sets, Mitteilungen Math. Sem. Giessen, Vol. 201 (1991) pp. 49–54.

    Google Scholar 

  2. H. L. Dorwart and B. Gruenbaum, Are these figures oximora?, Math. Magazine, Vol. 65, No. 3 (1992) pp. 158–169.

    Google Scholar 

  3. H. Gropp, Blocking set free configurations and their relations to digraphs and hypergraphs, Discrete Math., Vol. 165/166 (1997) pp. 359–370.

    Google Scholar 

  4. M. Funk, B. Jackson, D. Labbate and J. Sheehan, Det-extremal cubic bipartite graphs, J. Graph Theory, Vol. 44, No. 1 (2003) pp. 50–64.

    Google Scholar 

  5. M. Funk, B. Jackson, D. Labbate and J. Sheehan, 2–Factor hamiltonian graphs, Dedicated to Crispin St. J. A. Nash-Williams, J. Combin. Theory Ser. B, Vol. 87, No. 1 (2003) pp. 138–144.

    Google Scholar 

  6. M. Funk and D. Labbate, On minimally one-factorable r-regular bipartite graphs, Discrete Math., Vol. 216 (2000) pp. 121–137.

    Google Scholar 

  7. D. Goldschmidt, Automorphism of trivalent graphs, Ann. of Math. (2), Vol. 111, No. 2 (1980) pp. 377–406.

    Google Scholar 

  8. G. Higman, B. H. Neumann and H. Neumann, Embedding theorems for groups, J. London Math. Soc., Vol. 24 (1949) pp. 247–254.

    Google Scholar 

  9. O. H. Kegel and A. Schleiermacher, Amalgams and embeddings of projective planes, Geometriae Dedicata, Vol. 2 (1973) pp. 379–395.

    Google Scholar 

  10. D. Labbate, On determinants and permanents of minimally 1–factorable cubic bipartite graphs, Note Mat., Vol. 20, No. 1 (2000/01) pp. 37–42.

    Google Scholar 

  11. D. Labbate, On 3–cut reductions of minimally 1–factorable cubic bigraphs, Discrete Math., Vol. 231 (2001) pp. 303–310.

    Google Scholar 

  12. D. Labbate, Characterizing minimally 1–factorable r-regular bipartite graphs, Discrete Math., Vol. 248, No. 1–3 (2002) pp. 109–123.

    Google Scholar 

  13. W. McCuaig, Even dicycles, J. Graph Theory, Vol. 35 (2000) pp. 46–68.

    Google Scholar 

  14. Serre, Jean-Pierre Arbres, amalgames, SL2. Astèrisque, No. 46. Société Mathématique de France, Paris (1977).

    Google Scholar 

  15. C. Thomassen, Sign-nonsingular matrices and even cycles in directed graphs, Linear Algebra Appl., Vol. 75 (1986) pp. 27–41.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Labbate, D. Amalgams of Cubic Bipartite Graphs. Designs, Codes and Cryptography 32, 267–275 (2004). https://doi.org/10.1023/B:DESI.0000029229.06512.83

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/B:DESI.0000029229.06512.83

Navigation