Density Conditions For Triangles In Multipartite Graphs

@article{Bondy2006DensityCF,
  title={Density Conditions For Triangles In Multipartite Graphs},
  author={John Adrian Bondy and Jian Shen and St{\'e}phan Thomass{\'e} and Carsten Thomassen},
  journal={Combinatorica},
  year={2006},
  volume={26},
  pages={121-131}
}
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 17|V (G)|/20, 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… CONTINUE READING
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