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.
Why bother? A saturation number or a Zarankiewicz number is a claim that some graph exists, and the honest form of that claim is the graph itself. A paper can report the number. The House of Graphs lets anyone fetch the witness, decode it, and check it. The value stops being something you take on trust.
I found each witness by SAT solving or exhaustive enumeration, then re-verified it from scratch against its own graph6 encoding before depositing it.
Two of the three Zarankiewicz witnesses need careful wording. The matrix condition forbids a 3-by-4 all-ones submatrix (three rows, four columns), but the House of Graphs stores graphs unlabeled and forgets which side was rows. Those two graphs contain a K_{3,4} the other way around, so I describe them by the matrix condition, not as “K_{3,4}-free”. Only the third, z(9, 11; 3, 4) = 66, is genuinely K_{3,4}-free. An earlier description of mine got this wrong; the public entries now carry the correction.
I also 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). These two are verified and ready to deposit, but not deposited yet.
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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