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Spanning 3-ended trees in k-connected K 1,4-free graphs

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Abstract

A tree with atmost m leaves is called an m-ended tree. Kyaw proved that every connected K 1,4-free graph with σ 4(G) ⩽ n−1 contains a spanning 3-ended tree. In this paper we obtain a result for k-connected K 1,4-free graphs with k ⩽ 2. Let G be a k-connected K 1,4-free graph of order n with k ⩽ 2. If σ k+3(G) ⩽ n+2k −2, then G contains a spanning 3-ended tree.

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References

  1. Broersma H, Tuinstra H. Independence trees and Hamilton cycles. J Graph Theory, 1998, 29: 227–237

    Article  MATH  MathSciNet  Google Scholar 

  2. Chen G T, Schelp R. Hamiltonicity for K 1,4-free Graphs. J Graph Theory, 1995, 20: 423–439

    Article  MATH  MathSciNet  Google Scholar 

  3. Diestel R. Graph Theory, 3rd ed. Berlin: Springer, 2005

    MATH  Google Scholar 

  4. Flandrin E, Kaiser T, Kuzel R, et al. Neighborhood unions and extremal spanning trees. Discrete Math, 2008, 308: 2343–2350

    Article  MATH  MathSciNet  Google Scholar 

  5. Kano M, Kyaw A, Matsuda H, et al. Spanning trees with a bounded number of leaves in a claw-free graph. Ars Combin, 2012, 103: 137–154

    MATH  MathSciNet  Google Scholar 

  6. Kyaw A. Spanning trees with at most 3 leaves in K 1,4-free graphs. Discrete Math, 2009, 309: 6146–6148

    Article  MATH  MathSciNet  Google Scholar 

  7. Kyaw A. Spanning trees with at most k leaves in K 1,4-free graphs. Discrete Math, 2011, 311: 2135–2142

    Article  MATH  MathSciNet  Google Scholar 

  8. Matthews M, Sumner D. Hamiltonian results in K 1,3-free graphs. J Graph Theory, 1984, 8: 139–146

    Article  MATH  MathSciNet  Google Scholar 

  9. Ore O. Hamiltoian connected graphs. J Math Pure Appl, 1963, 42: 21–27

    MATH  MathSciNet  Google Scholar 

  10. Ozeki K, Yamashita T. Spanning trees: A survey. Graphs Combin, 2011, 27: 1–26

    Article  MATH  MathSciNet  Google Scholar 

  11. Win S. On a conjecture of Las Vergnas concerning certain spanning trees in graphs. Result Math, 1979, 2: 215–224

    Article  MATH  MathSciNet  Google Scholar 

  12. Zhang C Q. Hamilton cycle in Claw-free graphs. J Graph Theory, 1988, 12: 209–216

    Article  MATH  MathSciNet  Google Scholar 

Download references

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Authors and Affiliations

  1. Faculty of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, China

    Yuan Chen & ZhiQuan Hu

  2. College of Mathematics and Computer Science, Wuhan Textile University, Wuhan, 430073, China

    Yuan Chen

  3. Department of Mathematics and Statistics, Georgia State University, Atlanta, GA, 30303, USA

    GuanTao Chen

Authors
  1. Yuan Chen
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  2. GuanTao Chen
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  3. ZhiQuan Hu
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Correspondence to Yuan Chen.

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Chen, Y., Chen, G. & Hu, Z. Spanning 3-ended trees in k-connected K 1,4-free graphs. Sci. China Math. 57, 1579–1586 (2014). https://doi.org/10.1007/s11425-014-4817-z

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  • DOI: https://doi.org/10.1007/s11425-014-4817-z

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