### Abstract

A hamiltonian square-path (-cycle) is one obtained from a hamiltonian path (cycle) by joining every pair of vertices of distance two in the path (cycle). Let G be a graph on n vertices with minimum degree δ(G). Posá and Seymour conjectured that if δ(G) ≥ 2/3n, then G contains a hamiltonian square-cycle. We prove that if δ(G) ≥ (2n - 1)/3, then G contains a hamiltonian square-path. A consequence of this result is a theorem of Aigner and Brandt that confirms the case △(H) = 2 of the Bollabás-Eldridge Conjecture: if G and H are graphs on n vertices and (△(G) + 1)(△(H) + 1) ≤ n + 1, then G and H can be packed.

Original language | English (US) |
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Pages (from-to) | 167-182 |

Number of pages | 16 |

Journal | Journal of Combinatorial Theory. Series B |

Volume | 67 |

Issue number | 2 |

DOIs | |

State | Published - Jul 1996 |

### ASJC Scopus subject areas

- Theoretical Computer Science
- Discrete Mathematics and Combinatorics
- Computational Theory and Mathematics

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## Cite this

Fan, G., & Kierstead, H. (1996). Hamiltonian square-paths.

*Journal of Combinatorial Theory. Series B*,*67*(2), 167-182. https://doi.org/10.1006/jctb.1996.0039