Skip to main content
SpringerLink
Log in

On Enomoto’s problems in a bipartite graph

  • Published:
Science in China Series A: Mathematics Aims and scope Submit manuscript

Abstract

In this paper, we obtain the following result: Let k, n 1 and n 2 be three positive integers, and let G = (V 1,V 2;E) be a bipartite graph with |V1| = n 1 and |V 2| = n 2 such that n 1 ⩾ 2k + 1, n 2 ⩾ 2k + 1 and |n 1 − n 2| ⩽ 1. If d(x) + d(y) ⩾ 2k + 2 for every x ∈ V 1 and y ∈ V 2 with xy \( \notin \) E(G), then G contains k independent cycles. This result is a response to Enomoto’s problems on independent cycles in a bipartite graph.

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. The second edition. New York: Springer, 2008

    Google Scholar 

  2. Corrádi K, Hajnal A. On the maximal number of independent circuits in a graph. Acta Math Acad Sci Hungar, 14: 423–439 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  3. Wang H. On the maximum number of independent cycles in a bipartite graph. J Combin Theory Ser B, 67: 152–164 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  4. Enomoto H. Graph partition problems into cycles and paths. Discrete Math, 233: 93–101 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  5. Wang H. Large vertex-disjoint cycles in a bipartite graph. Graph Combin, 16: 359–366 (2000)

    Article  MATH  Google Scholar 

  6. Wang H. Proof of a conjecture on cycles in a bipartite graph. J Graph Theory, 31: 333–343 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  7. Wang H. On 2-factors of a bipartite graph. J Graph Theory, 31: 101–106 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  8. Li X, Wei B, Yang F. Independent cycles in a bipartite graph. Ars Combin, 73: 173–186 (2004)

    MATH  MathSciNet  Google Scholar 

  9. Yan J. Disjoint triangles and quadrilaterals in a graph. Discrete Math, 308: 3930–3937 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  10. Yan J, Liu G. On 2-factors with prescribed properties in a bipartite graph. Acta Math Sinica, English Ser, 15: 1–11 (2006)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mathematics, Shandong University, Jinan, 250100, China

    Jin Yan & YunShu Gao

Authors
  1. Jin Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. YunShu Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jin Yan.

Additional information

This work was supported by the Foundation for the Distinguished Young Scholars of Shandong Province (Grant No. 2007BS01021), the Taishan Scholar Fund from Shandong Province, SRF for ROCS, SEM and National Natural Science Foundation of China (Grant No. 60673047)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yan, J., Gao, Y. On Enomoto’s problems in a bipartite graph. Sci. China Ser. A-Math. 52, 1947–1954 (2009). https://doi.org/10.1007/s11425-009-0012-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11425-009-0012-z

Keywords

MSC(2000)

Search

Navigation