The generalized Ramsey number f(n, 5, 8) = frac 67 n + o(n)
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A $(p, q)$-coloring of $K_n$ is a coloring of the edges of $K_n$ such that every $p$-clique has at least $q$ distinct colors among its edges. The generalized Ramsey number $f(n, p, q)$ is the minimum number of colors such that $K_n$ has a $(p, q)$-coloring. Gomez-Leos, Heath, Parker, Schweider and Zerbib recently proved $f(n, 5, 8) \ge \frac 67 (n-1)$. Here we prove an asymptotically matching upper bound.
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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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