A note on total excess of spanning trees

Yukichika Ohnishi, Katsuhiro Ota

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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 languageEnglish
Pages (from-to)97-103
Number of pages7
JournalAKCE International Journal of Graphs and Combinatorics
Issue number1
Publication statusPublished - 2011 Jun 1
Externally publishedYes


  • Spanning trees
  • Total excess
  • Toughness

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics


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