Skip to main content
SpringerLink
Log in

The Distance Matching Extension in K1,k-free Graphs with High Local Connectedness

  • Published:
Acta Mathematicae Applicatae Sinica, English Series Aims and scope Submit manuscript

Abstract

A matching is extendable in a graph G if G has a perfect matching containing it. A distance q matching is a matching such that the distance between any two distinct matching edges is at least q. In this paper, we prove that any distance 2k − 3 matching is extendable in a connected and locally (k − 1)-connected K1,k-free graph of even order. Furthermore, we also prove that any distance q matching M in an r-connected and locally (k − 1)-connected K1,k-free graph of even order is extendable provided that ∣M∣ is bounded by a function on r, k and q. Our results improve some results in [J. Graph Theory 93 (2020), 5–20].

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. Aldred, R.E.L., Fujisawa, J., Saito, A. Distance matching extension and local structure of graphs. J. Graph Theory, 93: 5–20 (2020)

    Article  MathSciNet  Google Scholar 

  2. Aldred, R.E.L., Plummer, M.D. Matching extension in prism graphs. Discrete Appl. Math., 22: 125–32 (2017)

    MathSciNet  MATH  Google Scholar 

  3. Aldred, R.E.L., Plummer, M.D. Proximity thresholds for matching extension in planar and projective planar triangulations. J. Graph Theory, 67: 38–46 (2011)

    Article  MathSciNet  Google Scholar 

  4. Chen, C. Matchings and matching extensions in graphs. Discrete Math., 186(1–3): 95–103 (1998)

    Article  MathSciNet  Google Scholar 

  5. Costa, M.-C., de Werra, D., Picouleau, C. Minimal graphs for matching extensions. Discrete Appl. Math., 234: 47–55 (2018)

    Article  MathSciNet  Google Scholar 

  6. Diestel, R. Graph Theory, the Fifth Edition. Springer, GTM 173, 2017

  7. Fujisawa, J., Segawa, K., Suzuki, Y. The matching extendability of optimal 1-planar graphs. Graphs Combin., 34: 1089–1099 (2018)

    Article  MathSciNet  Google Scholar 

  8. Fujisawa, J., Seno, H. Edge proximity and matching extension in projective planar graphs. J. Graph Theory, 95(3): 341–367 (2020)

    Article  MathSciNet  Google Scholar 

  9. Hackfeld, J., Koster, A.M.C.A. The matching extension problem in general graphs is co-NP-complete. J. Comb. Optim., 35(3): 853–859 (2018)

    Article  MathSciNet  Google Scholar 

  10. Metsidik, M., Vumar, E. Toughness and matching extension in P3-dominated graphs. Graphs Combin., 26(3): 425–432 (2010)

    Article  MathSciNet  Google Scholar 

  11. Oberly, D.J., Sumner, D.P. Every connected, locally connected nontrivial graph with no induced claw is Hamiltonian. J. Graph Theory, 3: 351–356 (1979)

    Article  MathSciNet  Google Scholar 

  12. Plummer, M.D. Extending matchings in planar graphs IV. Discrete Math., 109: 207–219 (1992)

    Article  MathSciNet  Google Scholar 

  13. Plummer, M.D. Matching extension and the genus of a graph. J. Combin. Theory Ser. B, 44(3): 329–337 (1988)

    Article  MathSciNet  Google Scholar 

  14. Plummer, M.D. Toughness and matching extension in graphs. Discrete Math., 72(1–3): 311–320 (1988)

    Article  MathSciNet  Google Scholar 

  15. Ryjáček, Z. Matching extension in K1,r-free graphs with independent claw centers. Discrete Math., 164(1–3): 257–263 (1997)

    Article  MathSciNet  Google Scholar 

  16. Walcher, K.L. Matching extension in the powers of n-connected graphs. J. Graph Theory, 23(4): 355–360 (1996)

    Article  MathSciNet  Google Scholar 

  17. Yang, F., Yuan, J.J. IM-extendable claw-free graphs. J. Math. Study, 32(1): 33–37 (1999)

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

The authors thank Tong Li and Zhiheng Zhou for their helpful discussions, and appreciate the referees for their careful reading and valuable comments.

Funding

Supported in part by the National Natural Science Foundation of China (11631014) and the National Key Research & Development Program of China (2017YFC0908405).

Author information

Authors and Affiliations

  1. Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Wei-chan Liu & Gui-ying Yan

  2. University of Chinese Academy of Sciences, Beijing, 100049, China

    Wei-chan Liu & Gui-ying Yan

Authors
  1. Wei-chan Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gui-ying Yan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Gui-ying Yan.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, Wc., Yan, Gy. The Distance Matching Extension in K1,k-free Graphs with High Local Connectedness. Acta Math. Appl. Sin. Engl. Ser. 38, 37–43 (2022). https://doi.org/10.1007/s10255-022-1069-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10255-022-1069-6

Keywords

2000 MR Subject Classification

Search

Navigation