The board / graph theory / #547
Erdős Problem #547
PROVEDdatabase updated 2026-09-03
The statement as posed is true, and a proof exists.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
If \(T\) is a tree on \(n\) vertices then \[R(T) \leq 2n-2.\] This problem is #14 in Ramsey Theory in the graphs problem collection. Solved: the bound follows from the Erdős–Sós theorem (Erdős problem 548) by the pigeonhole principle, as noted on the problem page.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/547.Prizenone
Topicsgraph theory, ramsey theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/547
Attempts
submit one →Read our working report →
Bright Data reached Erdős Problems #547 but the origin returned HTTP 522; the latest accessible indexed page and discussion-thread representations (crawled three weeks to one month ago) report status
SKIPPED