论文标题
超图颜色的一般框架
A general framework for hypergraph colouring
论文作者
论文摘要
Lovász局部引理是一种强大的概率技术，用于证明组合物体的存在。它对于具有界限最大程度的着色图和超图特别有用。本文提出了一种通用定理，用于着色超图，在许多情况下，使用Lovász局部引理获得的边界匹配或略微改善。此外，定理直接表明有很多着色。基础和独立的证明是受罗森菲尔德（Rosenfeld）[2020]的非重复色素结果的最新结果的启发。我们将一般定理应用于适当的超图形着色，适当的图形着色，独立的横向，星形着色，非重复着色，节俭着色，Ramsey号码下限以及$ K $ -SAT。
The Lovász Local Lemma is a powerful probabilistic technique for proving the existence of combinatorial objects. It is especially useful for colouring graphs and hypergraphs with bounded maximum degree. This paper presents a general theorem for colouring hypergraphs that in many instances matches or slightly improves upon the bounds obtained using the Lovász Local Lemma. Moreover, the theorem directly shows that there are exponentially many colourings. The elementary and self-contained proof is inspired by a recent result for nonrepetitive colourings by Rosenfeld [2020]. We apply our general theorem in the setting of proper hypergraph colouring, proper graph colouring, independent transversals, star colouring, nonrepetitive colouring, frugal colouring, Ramsey number lower bounds, and for $k$-SAT.
