Toughness and Triangle-Free Graphs
β Scribed by D. Bauer; J. Vandenheuvel; E. Schmeichel
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 520 KB
- Volume
- 65
- Category
- Article
- ISSN
- 0095-8956
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
We show that for every k β₯ 1 and Ξ΄ > 0 there exists a constant c > 0 such that, with probability tending to 1 as n β β, a graph chosen uniformly at random among all triangle-free graphs with n vertices and M β₯ cn 3/2 edges can be made bipartite by deleting Ξ΄M edges. As an immediate consequence of th
For given n, let G be a triangle-free graph of order n with chromatic number at least 4. In this paper, we shall prove a conjecture of H/iggkvist by determining the maximal value of 6(G).
We study the cycle structure of I-tough, triangle-free graphs. In particular, w e prove that every such graph on n 2 3 vertices with minimum degree 6 2 i ( n + 2) has a 2-factor. W e also show this is best possible by exhibiting an infinite class of I-tough, triangle-free graphs having 6 = $ ( n + 1
Bollobas, B. and H.R. Hind, Graphs without large triangle free subgraphs, Discrete Mathematics 87 (1991) 119-131. The main aim of the paper is to show that for 2 < r <s and large enough n, there are graphs of order n and clique number less than s in which every set of vertices, which is not too sma