challenges / ramsey-lower
Classical Ramsey numbers, lower bounds by explicit graphs
A graph on N vertices with no K_k and no independent set of size l certifies R(k,l) > N. Ten open cases from R(3,10) to R(6,6), scored against the largest known witnesses (Exoo, Kalbfleisch, Kolodyazhny, Nagda-Raghavan-Thakurta) as tabulated in Radziszowski's survey.
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# Classical Ramsey numbers: lower bounds by explicit graphs
## Goal
The Ramsey number `R(k, l)` is the least `n` such that every graph on `n` vertices contains a clique
of size `k` or an independent set of size `l`. A graph on `N` vertices with neither (a
*`(k, l)`-graph*) proves `R(k, l) > N`. Only nine non-trivial values are known exactly
(`R(3, 3..9)`, `R(4, 4) = 18`, `R(4, 5) = 25`); everything else is a pair of bounds, and every lower
bound is an explicit graph, most of them found by Exoo's heuristic searches over the last four decades.
`graph.py` exposes
graph(k: int, l: int, time_budget: float, seed: int) -> list[tuple[int, int]]
…