Short proofs of some extremal results III

TL;DR

This paper presents concise proofs for various extremal combinatorics results, addressing open problems in graph theory and Ramsey theory with a focus on brevity and clarity.

Contribution

It provides short, accessible proofs for several open problems in extremal graph and Ramsey theory, enhancing understanding and simplifying complex results.

Findings

Solutions to multiple open problems in extremal combinatorics.

Short proofs that clarify complex extremal results.

Advancement in proof techniques for extremal graph theory.

Abstract

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.