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Conlon 2023 ramsey numbers zarankiewicz problem
David Conlon, Sam Mattheus, Dhruv Mubayi, Jacques Verstraëte, Ramsey numbers and the Zarankiewicz problem. Bull. Lond. Math. Soc. 56 (2024), no. 6, 2014--2023, doi:10.1112/blms.13040 (Crossref record read; the journal version was not compared); arXiv:2307.08694 (v1 17 July 2023, v2 24 April 2024). The arXiv record names arXiv's non-exclusive distribution license (arXiv:2307.08694), every other right reserved.
Following the approach Mattheus and Verstraete used for r(K_4,t) (p. 1), the paper ties the Ramsey numbers r(F,t), for a fixed graph F, to a matrix form of the Zarankiewicz problem in which the forbidden submatrices form a finite family L(F) built from F. It applies the link to the 5-cycle and the 7-cycle, with lower bounds for r(C_5,t) and r(C_7,t) of orders t^{10/7} and t^{5/4} up to logarithmic factors, and shows that a conjecture on Zarankiewicz numbers, if true, would determine r(C_{2l+1},t) approximately for every fixed l at least 2. The copy read for this card is arXiv:2307.08694v2, stamped 24 Apr 2024, 9 pages with a text layer; the arXiv listing showed no journal reference on 2026-09-17. Only the abstract and the opening of the introduction (p. 1) have been read, in the text layer, so no theorem is recorded here; problem 159 cites the abstract's C_5 and C_7 lower bounds as adjacent results. The paper's Zarankiewicz problem is the matrix number for the finite family L(F) of matrices derived from F (the abstract; p. 1 defines z(m, n, A) for a single matrix A), and it states no bound on ex(n; K_{r,r}). For problem 714 it is related activity connecting Ramsey numbers to Zarankiewicz-type extremal bounds, not progress on the problem's lower bound.
Source: https://arxiv.org/abs/2307.08694.
Bears on. #714; #159: the abstract's lower bounds for r(C_5,t) and r(C_7,t), odd cycles against cliques, adjacent to that problem's four-cycle question and not progress on it.
No file of this source is held: no license on record permits its redistribution, and the card cites the edition it names above.