On the asymptotic structure of sparse triangle free graphs
Journal of Graph Theory
Random Structures & Algorithms
The perturbation method and triangle-free random graphs
Proceedings of the seventh international conference on Random structures and algorithms
Szemerédi's regularity lemma for sparse graphs
FoCM '97 Selected papers of a conference on Foundations of computational mathematics
On triangle-free random graphs
Random Structures & Algorithms
Almost all graphs with high girth and suitable density have high chromatic number
Journal of Graph Theory
On extremal subgraphs of random graphs
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Generating random graphs with large girth
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Extremal subgraphs of random graphs
Random Structures & Algorithms
| Hi-index | 0.00 |
Let ${\cal T}(n,m)$ denote the set of all labelled triangle-free graphs with $n$ vertices and exactly $m$ edges. In this paper we give a short self-contained proof of the fact that there exists a constant $C0$ such that, for all $m\geq Cn^{3/2}\sqrt{\log n}$, a graph chosen uniformly at random from ${\cal T}(n,m)$ is with probability $1-o(1)$ bipartite.