EQUIVALENCE OF THE STRENGTHENED HANNA-NEUMANN CONJECTURE AND THE AMALGAMATED GRAPH CONJECTURE

• 成果类型: Article
• 署名作者: DICKS, W
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/BF01232249
• 发表日期: 1994
• 页码: 373-389
• 关键词: finitely generated subgroups; intersections

摘要

We show that Walter Neumann's strengthened form of Hanna Neumann's conjecture on the best possible upper bound for the rank of the intersection of two subgroups of a free group is equivalent to a conjecture on the best possible upper bound for the number of edges in a bipartite graph with a certain weak symmetry condition. We illustrate the usefulness of this equivalence by deriving relatively easily certain previously known results.