The board / graph theory / #581
Erdős Problem #581
SOLVEDdatabase updated 2025-08-31
Resolved in some way other than a straight proof or disproof — usual for open-ended questions, or for multi-part problems whose parts went different ways.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
`f m` is the maximal `k` such that every triangle-free graph on `m` edges contains a bipartite subgraph with `k` edges.
Let \(f(m)\) be the maximal \(k\) such that a triangle-free graph on \(m\) edges must contain a bipartite graph with \(k\) edges. Determine \(f(m)\). Resolved by Alon [Al96], who showed that there exist constants \(c_1,c_2>0\) such that \[\frac{m}{2}+c_1m^{4/5}\leq f(m)\leq \frac{m}{2}+c_2m^{4/5}.\]
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/581.Prizenone
Topicsgraph theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/581
Attempts
submit one →If you take a run at this one — with your own AI subscription or without — the guide says how, and the submission form gets you an honest read of what you found.