### Abstract

A graph G is said to be t-tough if ⌋ S ⌊ ≥ t. ω(G-S) for any subset S of V (G) with ω(G-S) ≥ 2, where ω(G-S) is the number of components in G-S. In this paper, we investigate t-tough graphs including the cases. Using the notion of total excess. We also investigate the relation between spanning trees in a graph obtained by different pairs of parameters (n, ε). As a consequence, we prove the existence of "a universal tree" in a connected t-tough graph G, that is a spanning tree T.

Original language | English |
---|---|

Pages (from-to) | 97-103 |

Number of pages | 7 |

Journal | AKCE International Journal of Graphs and Combinatorics |

Volume | 8 |

Issue number | 1 |

Publication status | Published - 2011 Jun |

Externally published | Yes |

### Fingerprint

### Keywords

- Spanning trees
- Total excess
- Toughness

### ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics

### Cite this

*AKCE International Journal of Graphs and Combinatorics*,

*8*(1), 97-103.

**A note on total excess of spanning trees.** / Ohnishi, Yukichika; Ota, Katsuhiro.

Research output: Contribution to journal › Article

*AKCE International Journal of Graphs and Combinatorics*, vol. 8, no. 1, pp. 97-103.

}

TY - JOUR

T1 - A note on total excess of spanning trees

AU - Ohnishi, Yukichika

AU - Ota, Katsuhiro

PY - 2011/6

Y1 - 2011/6

N2 - A graph G is said to be t-tough if ⌋ S ⌊ ≥ t. ω(G-S) for any subset S of V (G) with ω(G-S) ≥ 2, where ω(G-S) is the number of components in G-S. In this paper, we investigate t-tough graphs including the cases. Using the notion of total excess. We also investigate the relation between spanning trees in a graph obtained by different pairs of parameters (n, ε). As a consequence, we prove the existence of "a universal tree" in a connected t-tough graph G, that is a spanning tree T.

AB - A graph G is said to be t-tough if ⌋ S ⌊ ≥ t. ω(G-S) for any subset S of V (G) with ω(G-S) ≥ 2, where ω(G-S) is the number of components in G-S. In this paper, we investigate t-tough graphs including the cases. Using the notion of total excess. We also investigate the relation between spanning trees in a graph obtained by different pairs of parameters (n, ε). As a consequence, we prove the existence of "a universal tree" in a connected t-tough graph G, that is a spanning tree T.

KW - Spanning trees

KW - Total excess

KW - Toughness

UR - http://www.scopus.com/inward/record.url?scp=79961142816&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79961142816&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:79961142816

VL - 8

SP - 97

EP - 103

JO - AKCE International Journal of Graphs and Combinatorics

JF - AKCE International Journal of Graphs and Combinatorics

SN - 0972-8600

IS - 1

ER -