### Abstract

A graph G has a tank-ring factor F if F is a connected spanning subgraph with all vertices of degree 2 or 4 that consists of one cycle C and disjoint triangles attaching to exactly one vertex of C such that every component of G − C contains exactly two vertices. In this paper, we show the following results. (1) Every supereulerian claw-free graph G with 1-hourglass property contains a tank-ring factor. (2) Every supereulerian claw-free graph with 2-hourglass property is Hamiltonian.

Original language | Undefined |
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Pages (from-to) | 599-608 |

Number of pages | 10 |

Journal | Graphs and combinatorics |

Volume | 29 |

Issue number | 3 |

DOIs | |

Publication status | Published - 2013 |

### Keywords

- MSC-05C
- EWI-23369
- Claw-free graph
- IR-86130
- Hourglass property
- METIS-297653
- Hamiltonian graph

## Cite this

Li, M., Yuan, L., Jiang, H., Liu, B., & Broersma, H. J. (2013). Tank-ring factors in supereulerian claw-free graphs.

*Graphs and combinatorics*,*29*(3), 599-608. https://doi.org/10.1007/s00373-011-1117-z