A proof of the Erdo?s-Faber-Lov'asz conjecture

• 成果类型: Article
• 署名作者: Kang, Dong Yeap; Kelly, Tom; Kuhn, Daniela; Methuku, Abhishek; Osthus, Deryk
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2023.198.2.2
• 发表日期: 2023
• 页码: 537-618
• 关键词: coloring graphs; chromatic index; hypergraphs; decompositions; number

摘要

The Erdo ˝s-Faber-Lovasz conjecture (posed in 1972) states that the chromatic index of any linear hypergraph on n vertices is at most n. In this paper, we prove this conjecture for every large n. We also provide stability versions of this result, which confirm a prediction of Kahn.