Density theorems for bipartite graphs and related Ramsey-type results

Details Density theorems for bipartite graphs and related Ramsey-type results Density theorems for bipartite graphs and related Ramsey-type results

2007-07-27

arxiv.org/abs/0707.4159v2

Mathematics

Combinatorics

Scientific paper

In this paper, we present several density-type theorems which show how to find a copy of a sparse bipartite graph in a graph of positive density. Our results imply several new bounds for classical problems in graph Ramsey theory and improve and generalize earlier results of various researchers. The proofs combine probabilistic arguments with some combinatorial ideas. In addition, these techniques can be used to study properties of graphs with a forbidden induced subgraph, edge intersection patterns in topological graphs, and to obtain several other Ramsey-type statements.

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