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declared open (Lean) · formalized · $500erdos:146
If HH is bipartite and rr-degenerate, is ex(n;H)≪n2−1/r\mathrm{ex}(n;H) \ll n^{2-1/r} (a $500 Erdős-Simonovits prize conjecture)? A counterexample refutes the degeneracy conjecture.
graph theoryturan numberN/A3 sources
declared open (Lean) · formalizederdos:180
For every finite family F\mathcal{F} of graphs, is there a single G∈FG \in \mathcal{F} with ex(n;G)≪Fex(n;F)\mathrm{ex}(n;G) \ll_{\mathcal{F}} \mathrm{ex}(n;\mathcal{F})? A counterexample refutes the Erdős-Simonovits compactness conjecture.
graph theoryturan numberN/A4 sources
declared open (Lean) · formalized · $250erdos:183
Let R(3;k)R(3;k) be the least nn such that every kk-colouring of the edges of KnK_n contains a monochromatic triangle. Determine lim⁡k→∞R(3;k)1/k\lim_{k\to\infty} R(3;k)^{1/k} (a $250 Erdős prize problem). A superexponential lower bound resolves the problem: the limit is infinite.
graph theoryramsey theoryA0033233 sources
declared open (Lean)erdos:1112
Erdős problem 1112
additive combinatoricsN/A

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