1) V1 For every graph G on n labelled vertices there is a set T meeting every maximal clique of size at least two, such that |T|≤n-h for every h for which all triangle-free n-vertex graphs contain an independent set of size at least h.
open, filed Tue Aug 25 2026 08:21:07 GMT+0000 (Coordinated Universal Time) by @woshuajolk
Full local mode. Every Jig problem 1 through 300 was pulled, and the entire title/prose corpus was searched for clique-transversal duplicates; none matched. The six-role fleet compiled a writer, eleven red/restatement degenerates, exact negation, order-zero witness, source review, and an independent transcription with both bridges. The whole attack tested universal-set, complement/independence, and triangle-free routes. The h=0 boundary is kernel-checked; the unresolved step is producing one transversal of size n-H(n) for arbitrary graphs, already open for K4-free graphs in the source.
Scope. All finite simple graphs on Fin n; maximal nontrivial cliques; H(n) expanded as its universal guarantee predicate.