Skip to main content
SpringerLink
Log in

Nowhere-Zero 3-Flows of Graphs with Independence Number Two

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

Abstract

In this paper, we characterize all graphs with independence number at most 2 that admit nowhere-zero 3-flows.

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. Bondy J.A., Murty U.S.R.: Graph Theory with Applications. North-Holland, New York (1976)

    MATH  Google Scholar 

  2. Chen J.-J., Eschen E., Lai H.-J.: Group connectivity of certain graphs. Ars Combin. 89, 141–158 (2008)

    MathSciNet  MATH  Google Scholar 

  3. Chvátal V., Erdős P.: A note on Hamiltonian circuits. Discret. Math. 2, 111–113 (1972)

    Article  MATH  Google Scholar 

  4. Fan G., Zhou C.: Ore-condition and nowhere-zero 3-flow. SIAM J. Discret. Math. 22, 288–294 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  5. Fan G., Zhou C.: Degree sum and nowhere-zero 3-flows. Discret. Math. 308, 6233–6240 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Fan G., Lai H.-J., Xu R., Zhang C.-Q., Zhou C.: Nowhere-zero 3-flows in triangularly connected graphs. J. Combin. Theory Ser. B 98, 1325–1336 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  7. Jaeger F.: Flows and generalized coloring theorems in graphs. J. Combin. Theory Ser. B 26, 205–216 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  8. Luo R., Xu R., Zang W., Zhang C.-Q.: Realizing degree sequences with graphs having nowhere-zero 3-flows. SIAM J. Discret. Math. 22, 500–519 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  9. Luo, R., Miao, Z.-K., Xu, R., Zhang, C.-Q.: Nowhere-zero 3-flows of graphs with prescribed sizes of odd edge cuts (preprint)

  10. Luo R., Xu R., Yin J.-H., Yu G.: Ore-condition and Z 3-connectivity. Eur. J. Combin. 29, 1587–1595 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  11. Xu, R.: Two equivalent properties of Z 3-connectivity. Graphs Combin. doi:10.1007/s00373-012-1197-4

  12. Yin J.-H., Zhang Y.: Pósa-condition and nowhere-zero 3-flows. Discret. Math. 311, 897–907 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  13. Zhang X., Zhan M., Xu R., Shao Y., Li X., Lai H.-J.: Degree sum condition for Z3-connectivity in graphs. Discret. Math. 310, 3390–3397 (2010)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, West Virginia University, Morgantown, WV, 26506-6310, USA

    Rong Luo

  2. School of Mathematical Sciences, Jiangsu Normal University, Xuzhou, 221116, Jiangsu, China

    Zhengke Miao

  3. Department of Mathematics, University of West Georgia, Carrollton, GA, 30118, USA

    Rui Xu

Authors
  1. Rong Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zhengke Miao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Rui Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhengke Miao.

Additional information

R. Luo’s research was partially supported by NSF-China Grant: NSFC 11171228. Z. Miao’s research was partially supported by NSF-China Grants: NSFC 11171228 and NSFC 10871166. R. Xu’s research was partially supported by the 2011–2012 COSM Research Incentive Award of University of West Georgia.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Luo, R., Miao, Z. & Xu, R. Nowhere-Zero 3-Flows of Graphs with Independence Number Two. Graphs and Combinatorics 29, 1899–1907 (2013). https://doi.org/10.1007/s00373-012-1238-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00373-012-1238-z

Keywords

Search

Navigation