# Short proofs of some extremal results III

@article{Conlon2020ShortPO, title={Short proofs of some extremal results III}, author={David Conlon and Jacob Fox and Benny Sudakov}, journal={Random Structures \& Algorithms}, year={2020}, volume={57}, pages={958 - 982} }

We prove a selection of results from different areas of extremal combinatorics, including complete or partial solutions to a number of open problems. These results, coming mainly from extremal graph theory and Ramsey theory, have been collected together because in each case the relevant proofs are reasonably short.

## 7 Citations

### Ramsey numbers with prescribed rate of growth

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. Let R ( G ) be the two-colour Ramsey number of a graph G . In this note, we prove that for any non-decreasing function n 6 f ( n ) 6 R ( K n ), there exists a sequence of connected graphs ( G n ) n…

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Given a graph G , its Ramsey number r ( G ) is the minimum N so that every two-coloring of E ( K N ) contains a monochromatic copy of G . It was conjectured by Conlon, Fox, and Sudakov that if one…

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The Ramsey number r ( G, H ) is the minimum N such that every graph on N vertices contains G as a subgraph or its complement contains H as a subgraph. For integers n ≥ k ≥ 1, the k -book B k,n is the…

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A graph G is q-Ramsey for another graph H if in any q-edge-colouring of G there is a monochromatic copy of H, and the classic Ramsey problem asks for the minimum number of vertices in such a graph.…

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