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# 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} }

- Published in Combinatorica 2006
DOI:10.1007/s00493-006-0009-y

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