The board / graph theory / #549
Erdős Problem #549
DISPROVEDdatabase updated 2025-08-31
The statement as posed is false.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
If \(T\) is a tree which is a bipartite graph with \(k\) vertices in one class and \(2k\) vertices in the other class then \[R(T)=4k-1.\] This is false: Norin, Sun, and Zhao [NSZ16] have proved that if \(T\) is the union of two stars on \(k\) and \(2k\) vertices, with an edge joining the centre of the two stars, then \(R(T)\geq (4.2-o(1))k\), and conjectured that \(R(T)=(4.2+o(1))k\). This problem is #15 in Ramsey Theory in the graphs problem collection.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/549.Prizenone
Topicsgraph theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/549
Attempts
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