Two remarks on the Burr-Erdős conjecture
European Journal of Combinatorics
Hypergraph packing and sparse bipartite ramsey numbers
Combinatorics, Probability and Computing
Disjoint edges in complete topological graphs
Proceedings of the twenty-eighth annual symposium on Computational geometry
Erdős-Hajnal-type theorems in hypergraphs
Journal of Combinatorial Theory Series B
Density theorems for intersection graphs of t-monotone curves
GD'12 Proceedings of the 20th international conference on Graph Drawing
Topological graphs: empty triangles and disjoint matchings
Proceedings of the twenty-ninth annual symposium on Computational geometry
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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.