Skip to main content

Connectivity and Extendability in Digraphs

  • Conference paper
  • First Online:
Combinatorics, Graph Theory and Computing (SEICCGTC 2020)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 388))

  • 357 Accesses

Abstract

In this article we give several definitions of connectedness and extendability of paths and cycles in directed graphs. We define sets of digraphs by various types of connectedness or extendability and give some containments as well as give examples to show proper containment.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Alavi, Y., Williamson, J. E., “Panconnected graphs”, Studia Scientiarum Mathematicarum Hungarica, 10 (1975) Nos. 1–2: 19–22.

    MathSciNet  MATH  Google Scholar 

  2. Arangno, D. C., “Hamiltonicity, Pancyclicity, and Cycle Extendability in Graphs”, Utah State University (2014). All Graduate Theses and Dissertations. 3295. https://digitalcommons.usu.edu/etd/3295

  3. Beasley, L. B. and Brown, D. E., “On cycle and bi-cycle extendability in chordal and chordal bipartite graphs”, Congressus Numerantium. 174(2005)41–47.

    MathSciNet  MATH  Google Scholar 

  4. Beasley, L. B. and Brown, D. E., “Cycle extendability in graphs and digraphs”. Linear Algebra Appl. 435 (2011), no. 7, 1513–1519.

    Article  MathSciNet  Google Scholar 

  5. Beasley, L. B., Merz, S. K., Brown, D. E., and Thomas, B. J., “Cycle extendability in tournamendts”. Congressus Numerantium. 233 (2019), pp.95-101.

    Google Scholar 

  6. Chartrand, G. and Lesniak, L., Graphs and Digraphs, \(2^{nd}\)Ed., Wadswoth & Brooks/Cole, Monterey, CA, 1986

    Google Scholar 

  7. G. Chen, R.J. Faudree, R.J. Gould, M.S. Jacobson, “Cycle extendability of Hamiltonian interval graphs”, SIAM J. Discrete Math. 20(3) (2006) 682–689.

    Article  MathSciNet  Google Scholar 

  8. Hendry, G.R.T., “Extending Cycles in Directed Graphs”, J. Comb. Th. B., 46(1989) 162–172.

    Article  MathSciNet  Google Scholar 

  9. Hendry, G. R. T., “Extending cycles in graphs”, Discrete Math. 85 (1990) no. 1, 59 – 72.

    Article  MathSciNet  Google Scholar 

  10. Hendry, G. R. T., “Path extendable graphs”, Per. Math. Hungarica, 21(3, (1990), 205 – 219.

    Google Scholar 

  11. Lafond, M. and Seamone, B., “Hamiltonian chordal graphs are not cycle extendible”, SIAM J. Discrete Math. 29(2), (2015) 877–887.

    Article  MathSciNet  Google Scholar 

  12. J. W. Moon, Topics in Tournaments, Holt, New York, 1968.

    MATH  Google Scholar 

  13. J. W. Moon, “On cycles in Tournaments”, Matematicky Časopsis, 19(1969, No. 2, 121–125.

    Google Scholar 

  14. Zhang, Z.-B., Zhang, X., Broersma, H., and Lou, D., “Extremal and degree conditions for path extendability in digraphs”. SIAM J. Discrete Math. 31 (2017), no. 3, 1990–2014.

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to LeRoy B. Beasley .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Beasley, L.B. (2022). Connectivity and Extendability in Digraphs. In: Hoffman, F. (eds) Combinatorics, Graph Theory and Computing. SEICCGTC 2020. Springer Proceedings in Mathematics & Statistics, vol 388. Springer, Cham. https://doi.org/10.1007/978-3-031-05375-7_19

Download citation

Publish with us

Policies and ethics