### Abstract

Barnette proved that every 3-connected planar graph has a 3-tree, where a 3-tree is a spanning tree whose maximum degree is at most three. In this paper, we consider an improvement of Barnette's result for the direction of K_{3, t}-minor-free graphs. Note that any planar graph is K_{3, 3}-minor-free. Actually, we show that for an even integer t ≥ 3, any 3-connected K_{3, t} -minor-free graph has a (t - 1)-tree.

Original language | English |
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Pages (from-to) | 145-149 |

Number of pages | 5 |

Journal | Electronic Notes in Discrete Mathematics |

Volume | 34 |

DOIs | |

Publication status | Published - 2009 Aug 1 |

### Keywords

- K-minor-free graphs
- Planar graphs
- Spanning tree

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics

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## Cite this

Ota, K., & Ozeki, K. (2009). Spanning trees in 3-connected K

_{3,t}-minor-free graphs.*Electronic Notes in Discrete Mathematics*,*34*, 145-149. https://doi.org/10.1016/j.endm.2009.07.024