Establishes the first exponential improvement since 1947 to the lower bound on off-diagonal Ramsey numbers r(ℓ, Cℓ) for constant C > 1.
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4 Pith papers cite this work. Polarity classification is still indexing.
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Proves that graphs on N ≥ 2n vertices with δ(G) ≥ ⌊3N/4⌋ have every 2-edge-coloring containing a monochromatic copy of every n-vertex tree with max degree ≤ Δ.
New lower bounds r_odd(n, K_{s,t}) > n^{1/(s/2 + 1/(2 floor(t/8)))} for odd s even t, r_u(n, C_n) > n/4 creating a polynomial gap, and odd-Ramsey number of Hamilton cycles >1 in super-Dirac graphs.
Proves the k-color Ramsey number R_k(k+1,k+1) is at least 4 times a tower of height floor(k/4)-3.
citing papers explorer
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An exponential improvement for Ramsey lower bounds
Establishes the first exponential improvement since 1947 to the lower bound on off-diagonal Ramsey numbers r(ℓ, Cℓ) for constant C > 1.
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A degree version of the Burr-Erd\H{o}s conjecture on trees
Proves that graphs on N ≥ 2n vertices with δ(G) ≥ ⌊3N/4⌋ have every 2-edge-coloring containing a monochromatic copy of every n-vertex tree with max degree ≤ Δ.
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New results on the odd- and unique-Ramsey numbers
New lower bounds r_odd(n, K_{s,t}) > n^{1/(s/2 + 1/(2 floor(t/8)))} for odd s even t, r_u(n, C_n) > n/4 creating a polynomial gap, and odd-Ramsey number of Hamilton cycles >1 in super-Dirac graphs.
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A lower bound on the Ramsey number $R_k(k+1,k+1)$
Proves the k-color Ramsey number R_k(k+1,k+1) is at least 4 times a tower of height floor(k/4)-3.