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.

中文翻译：

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一些极端结果的简短证明III

我们证明了极端组合药不同领域的一系列结果，包括对许多未解决问题的完整或部分解决方案。这些结果主要来自极值图论和Ramsey理论，已被收集在一起，因为在每种情况下，相关的证明都相当短。