Additive Approximation for Edge-Deletion Problems
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
On the minimal degree implying equality of the largest triangle-free and bipartite subgraphs
Journal of Combinatorial Theory Series B
Bounded transversals in multipartite graphs
Journal of Graph Theory
| Hi-index | 0.00 |
We consider the problem of finding a large or dense triangle-free subgraph in a given graph G. In response to a question of P. Erdős, we prove that, if the minimum degree of G is at least 9|V (G)|/10, the largest triangle-free subgraphs are precisely the largest bipartite subgraphs in G. We investigate in particular the case where G is a complete multipartite graph. We prove that a finite tripartite graph with all edge densities greater than the golden ratio has a triangle and that this bound is best possible. Also we show that an infinite-partite graph with finite parts has a triangle, provided that the edge density between any two parts is greater than 1/2.