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3-Connected {K 1,3, P 9}-Free Graphs are Hamiltonian-Connected

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Abstract

We investigate pairs of forbidden subgraphs that imply a 3-connected graph is Hamiltonian-connected. In particular we show that the pair {K 1,3, P 9} is such a pair. As it is known that P 10 cannot replace P 9, this result is best possible. Further, we show that certain other graphs are not possible.

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Authors and Affiliations

  1. School of Mathematics and Information Science, Shandong University of Technology, Zibo, 50100, People’s Republic of China

    Qiuju Bian

  2. Department of Mathematics and Computer Science, Emory University, 400 Dowman Dr. W401, Atlanta, GA, 30322, USA

    Ronald J. Gould, Susan Janiszewski & Steven La Fleur

  3. Department of Mathematics, FAS, Harvard University, One Oxford Street, Cambridge, MA, 02138, USA

    Paul Horn

  4. Department of Mathematics, Western Kentucky University, 1906 College Heights Blvd #11078, Bowling Green, KY, 42101, USA

    Paul Wrayno

Authors
  1. Qiuju Bian
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  2. Ronald J. Gould
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  3. Paul Horn
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  4. Susan Janiszewski
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  5. Steven La Fleur
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  6. Paul Wrayno
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Correspondence to Steven La Fleur.

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Bian, Q., Gould, R.J., Horn, P. et al. 3-Connected {K 1,3, P 9}-Free Graphs are Hamiltonian-Connected. Graphs and Combinatorics 30, 1099–1122 (2014). https://doi.org/10.1007/s00373-013-1344-6

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  • DOI: https://doi.org/10.1007/s00373-013-1344-6

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