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16 problemsGraph view
declared open · $100erdos:78
Erdős problem 78
graph theoryramsey theoryA0594422 sources
declared open · $500erdos:161
Erdős problem 161
combinatoricsramsey theorydiscrepancyN/A2 sources
declared openerdos:335
Erdős problem 335
number theoryadditive combinatoricsN/A2 sources
declared openerdos:514
For a transcendental entire function, how fast can ∣f(z)∣|f(z)| be forced to grow along a path to infinity, and how short can such a path be in terms of the maximum modulus M(r,f)M(r, f)?
analysisN/A4 sources
declared openerdos:524
Erdős problem 524
analysisprobabilitypolynomialsN/A3 sources
declared openerdos:550
Let m1≤⋯≤mkm_1\leq\cdots\leq m_k and nn be sufficiently large. If TT is a tree on nn vertices and GG is the complete multipartite graph with vertex class sizes m1,…,mkm_1,\ldots,m_k, prove that R(T,G)≤(χ(G)−1)(R(T,Km1,m2)−1)+m1R(T,G)\leq (\chi(G)-1)(R(T,K_{m_1,m_2})-1)+m_1.
graph theoryramsey theoryN/A4 sources
declared openerdos:662
Among sufficiently large one-separated planar point sets, does the triangular lattice maximize the number of distances below each threshold? Explicit rational oblique lattices beat the triangular lattice under several closed- and strict-shell readings.
geometrydistancesN/A3 sources
declared openerdos:665
Erdős problem 665
combinatoricsN/A2 sources
declared openerdos:731
Let A(n)A(n) be the least positive integer not dividing (2nn)\binom{2n}{n}. Erdos asked for the behaviour of A(n)A(n) for reasonable nn. Under an explicit dyadic-regularity formalization of reasonable, the distribution is determined on dyadic intervals against the scale FX=2(log⁡2)1/4L1/4exp⁡(log⁡2)LF_X = \sqrt{2}(\log 2)^{1/4} L^{1/4} \exp\sqrt{(\log 2)L} with L=log⁡(2X)L = \log(2X).
number theorybinomial coefficientsA0061974 sources
declared openerdos:734
Erdős problem 734
combinatoricspossible2 sources
declared openerdos:788
Erdős problem 788
additive combinatoricspossible3 sources
declared openerdos:792
Erdős problem 792
additive combinatoricspossible2 sources
declared openerdos:864
Erdős problem 864
number theorysidon setsadditive combinatoricsA3891822 sources
declared openerdos:866
Estimate the least excess gk(N)g_k(N) forcing kk integers whose pairwise sums all lie in a dense subset of {1,…,2N}\{1, \dots, 2N\}; in particular, determine the positive variant h4(n)h_4(n).
number theoryadditive combinatoricspossible5 sources
declared openerdos:954
Erdős problem 954
number theoryA3906422 sources
declared openerdos:969
Erdős problem 969
number theoryA0139282 sources

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