### Abstract

Let M be a matching in a graph G such that d(x) + d(y) ≥ |G| for all pairs of independent vertices x and y of G that are incident with M. We determine a necessary and sufficient condition for M to be contained in a cycle of G. This extends results of Häggkvist and Berman, and implies that if M is a 1‐factor of G and |G| 0 (mod 4), then M is contained in a Hamilton cycle of G. We use our results to deduce that an eulerian graph of minimum degree 2k contains k pairwise compatible Euler tours.

Original language | English |
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Pages (from-to) | 127-138 |

Number of pages | 12 |

Journal | Journal of Graph Theory |

Volume | 14 |

Issue number | 1 |

DOIs | |

Publication status | Published - 1990 |

Externally published | Yes |

## Cite this

Jackson, B., & Wormald, N. C. (1990). Cycles containing matchings and pairwise compatible euler tours.

*Journal of Graph Theory*,*14*(1), 127-138. https://doi.org/10.1002/jgt.3190140114