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.
|Number of pages||7|
|Journal||AKCE International Journal of Graphs and Combinatorics|
|Publication status||Published - 2011 Jun 1|
- Spanning trees
- Total excess
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics