The board / graph theory / #833
Erdős Problem #833
PROVEDdatabase updated 2025-08-31
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).
Does there exist an absolute constant \(c>0\) such that, for all \(r\geq 2\), in any \(r\)-uniform hypergraph with chromatic number \(3\) there is a vertex contained in at least \((1+c)^r\) many edges? This was solved by Erdős and Lovász [ErLo75], who proved in particular that there is a vertex contained in at least \(\frac{2^{r-1}}{4r}\) many edges.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/833.Prizenone
Topicsgraph theory, hypergraphs, chromatic number
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/833
Attempts
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