Skip to main content
SpringerLink
Log in

Arc-Disjoint and Edge-Disjoint Hamilton Cycles in Circulants with Two Jumps

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

Abstract

In this paper we give new necessary and sufficient conditions for a directed circulant with vertices of outdegree two to have a pair of arc-disjoint Hamilton cycles. These conditions explicitly identify a pair of arc-disjoint Hamilton cycles if such cycles exist. In addition, we give necessary and sufficient conditions for an undirected circulant with vertices of degree four to have a specific pair of edge-disjoint Hamilton cycles.

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. Alspach B., Locke S., Witte D.: The Hamilton spaces of Cayley graphs on Abelian groups. Discret. Math. 82, 113–126 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  2. Bermond J.-C., Favaron O., Maheo M.: Hamiltonian decomposition of Cayley graphs of degree 4. J. Combin. Theory Ser. B. 46, 142–153 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  3. Boesch F.T., Tindell R.: Circulants and their connectivities. J. Graph Theory 8, 129–138 (1984)

    Article  MathSciNet  Google Scholar 

  4. Bogdanowicz Z.R.: Hamilton cycles in circulant digraphs with prescribed number of distinct jumps. Discret. Math. 309, 2100–2107 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  5. Bogdanowicz Z.R.: Pancyclicity of connected circulant graphs. J. Graph Theory. 22, 167–174 (1996)

    Article  MathSciNet  MATH  Google Scholar 

  6. Elspas B., Turner J.: Graphs with circulant adjacency matrices. J. Combin. Theory. 9, 297–307 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  7. Keating K.: Multiple Hamiltonian graphs and digraphs. Ann. Discret. Math. 27, 81–88 (1985)

    MathSciNet  Google Scholar 

  8. Lovász L.: Combinatorial Problems and Excersises. North-Holland, Amsterdam (1979)

    Google Scholar 

  9. Yang Q., Burkard R., Cela E., Woginger G.: Hamiltonian cycles in circulant digraphs with two stripes. Discret. Math. 176, 233–254 (1997)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Armament Research, Development and Engineering Center, Picatinny, NJ, 07806, USA

    Zbigniew R. Bogdanowicz

Authors
  1. Zbigniew R. Bogdanowicz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zbigniew R. Bogdanowicz.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bogdanowicz, Z.R. Arc-Disjoint and Edge-Disjoint Hamilton Cycles in Circulants with Two Jumps. Graphs and Combinatorics 29, 165–171 (2013). https://doi.org/10.1007/s00373-011-1107-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-011-1107-1

Keywords

Search

Navigation