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Problem 599
Let be a (possibly infinite) graph and be disjoint independent sets of vertices. Must there exist a family of disjoint paths between and and a set which contains exactly one vertex from each path in , and such that every path between and contains at least one vertex from ?
Source: erdosproblems.com/599
- Graph theory
- Set theory
Status
Solved, ProvedAn accepted solution exists. The statement is true.
Proved. The site's commentary credits Aharoni and Berger, and the frontmatter standing is derived from the accepted claim page Aharoni and Berger's infinite Menger theorem, accepted on its refereed publication and the site's credit.