I deposited four graphs to the House of Graphs: a minimum C6-saturated graph on 8 vertices, and three extremal bipartite graphs for the Zarankiewicz problem z(m, n; 3, 4). They are live as entries #57145, #56650, #56651, and #56652.
The reason to deposit them is simple. A graph saturation number or a Zarankiewicz number is an existence claim, and the honest form of the claim is a concrete graph. A paper can report the number; the House of Graphs lets anyone fetch the actual witness, decode it, and check the property for themselves. The value stops being something to take on trust.
Each witness was computed by SAT solving or exhaustive enumeration and re-verified from scratch against its own graph6 encoding before deposit. Two of the three Zarankiewicz witnesses need care in how they are described. House of Graphs stores graphs unlabeled, and those two contain a K_{3,4} in one orientation, so I describe them by the matrix condition they actually satisfy (no 3-by-4 all-ones submatrix) rather than as “K_{3,4}-free”. Only the third, z(9, 11; 3, 4) = 66, is genuinely K_{3,4}-free. That distinction came from catching an earlier description that was wrong; the correction is now in the public entries.
Alongside the deposits, I verified two new exact saturation values, sat(9, C6) = 12 and sat(10, C6) = 13, each with both certificates. They continue the n+3 pattern of the C6 chain (9, 10, 11, 12, 13 for n = 6 through 10). Those two are verified and prepared for deposit, not yet deposited.
The full write-up, with every witness and the certificates behind it, is at /research/hog/. The backing computations are in the saturation and Zarankiewicz papers (Zenodo 10.5281/zenodo.19985046 and 10.5281/zenodo.19985042).
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