graphs of order n and size at least t r (n) that do not have a vertex x of maximal degree d x whose neighbours span at least t r&1 (d x )+1 edges. Furthermore, we show that, for every graph G of order n and size at least t r (n), the degree-greedy algorithm used by Bondy (1983, J. Combin. Theory Ser
Turán theorems with repeated degrees
✍ Scribed by Michael O. Albertson
- Publisher
- Elsevier Science
- Year
- 1992
- Tongue
- English
- Weight
- 352 KB
- Volume
- 100
- Category
- Article
- ISSN
- 0012-365X
No coin nor oath required. For personal study only.
✦ Synopsis
The maximum number of edges in a graph with no constant degree clique of a fixed size is determined asymptotically.
📜 SIMILAR VOLUMES
## Abstract In this paper, we obtain an asymptotic generalization of Turán's theorem. We prove that if all the non‐trivial eigenvalues of a __d__‐regular graph __G__ on __n__ vertices are sufficiently small, then the largest __K__~__t__~‐free subgraph of __G__ contains approximately (__t__ − 2)/(__
## Abstract The minimum size of a __k__‐connected graph with given order and stability number is investigated. If no connectivity is required, the answer is given by Turán's Theorem. For connected graphs, the problem has been solved recently independently by Christophe et al., and by Gitler and Val
The theorems of Erdo s and Tura n mentioned in the title are concerned with the distribution of zeros of a monic polynomial with known uniform norm along the unit interval or the unit disk. Recently, Blatt and Grothmann (Const. Approx. 7 (1991), 19 47), Grothmann (``Interpolation Points and Zeros of