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- W2965971868 abstract "The Ramsey number (r_k(p, q)) is the smallest integer N that satisfies for every red-blue coloring on k-subsets of [N], there exist p integers such that any k-subset of them is red, or q integers such that any k-subset of them is blue. In this paper, we study the lower bounds for small Ramsey numbers on hypergraphs by constructing counter-examples and recurrence relations. We present a new algorithm to prove lower bounds for (r_k(k+1, k+1)). In particular, our algorithm is able to prove (r_5(6,6) ge 72), where there is no lower bound on 5-hypergraphs before this work. We also provide several recurrence relations to calculate lower bounds based on lower bound values on smaller p and q. Combining both of them, we achieve new lower bounds for (r_k(p, q)) on arbitrary p, q, and (k ge 4)." @default.
- W2965971868 created "2019-08-13" @default.
- W2965971868 creator A5067329945 @default.
- W2965971868 date "2019-01-01" @default.
- W2965971868 modified "2023-09-27" @default.
- W2965971868 title "Lower Bounds for Small Ramsey Numbers on Hypergraphs" @default.
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- W2965971868 doi "https://doi.org/10.1007/978-3-030-26176-4_34" @default.
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