\$ ./flagmatic --r 3 --n 7 --forbid-k4- --forbid-induced 4.1 --dir output/ff84 flagmatic version 1.5 ============================================================================ Forbidding 4.3 Forbidding 4.1 as an induced subgraph. Using admissible graphs of order 7. Generated 1 type of order 1, with 3 flags of order 4. Generated 2 types of order 3, with [14, 9] flags of order 5. Generated 4 types of order 5, with [16, 9, 7, 6] flags of order 6. Generated 10 admissible graphs. Approximate floating-point bound is 0.27777778 \$ sage -python scripts/find_sharp_graphs.py --dir output/ff84 Floating point bound is 0.277777779939706149. 9 members of H are sharp. 0.277777779378811540 : graph 1 (7:) 0.277777779387497259 : graph 2 (7:123124125126127) 0.277777779939706149 : graph 3 (7:123124125126137147157167) 0.277777779656864898 : graph 4 (7:123124125136137146147156157) 0.277777779558789739 : graph 5 (7:123124125126137147157267367467567) 0.277777779787379886 : graph 6 (7:123124125126137147257267357367457467) 0.277777779787393098 : graph 7 (7:123124125136146156237247257367467567) 0.277777779787340862 : graph 8 (7:123124125136137146147256257356357456457) 0.277777779101805511 : graph 10 (7:123124125136146157167237247256267356357456457) Written sharp graphs to flags.py \$ sage -python scripts/check_construction.py --n 7 --r 3 --vertex-transitive 6:123234345451512136246356256146 Density is 5/18. 9 graphs of order 7 occur as induced subgraphs of the blow-up: 7: has density 1663/23328 (0.071288) 7:123124125126127 has density 35/486 (0.072016) 7:123124125126137147157167 has density 175/864 (0.202546) 7:123124125136137146147156157 has density 1225/11664 (0.105024) 7:123124125126137147157267367467567 has density 175/1944 (0.090021) 7:123124125136146156237247257367467567 has density 175/1296 (0.135031) 7:123124125126137147257267357367457467 has density 175/1296 (0.135031) 7:123124125136137146147256257356357456457 has density 175/1296 (0.135031) 7:123124125136146157167237247256267356357456457 has density 35/648 (0.054012) \$ sage -python scripts/make_zero_eigenvectors.py --vertex-transitive 6:123234345451512136246356256146 --dir output/ff84 Constructed 1 out of 1 zero eigenvectors for type 1. Constructed 5 out of 5 zero eigenvectors for type 2. Constructed 1 out of 1 zero eigenvectors for type 3. Constructed 16 out of 16 zero eigenvectors for type 4. Constructed 4 out of 4 zero eigenvectors for type 5. Constructed 3 out of 3 zero eigenvectors for type 6. Constructed 1 out of 1 zero eigenvectors for type 7. Written zev.py Written field to flags.py \$ sage -python scripts/factor_approximate_q.py --dir output/ff84 Floating point bound is 0.277777779939706149. Type 1: smallest eigenvalue is 0.825935693251547587 Type 2: smallest eigenvalue is 0.229848238859588549 Type 3: smallest eigenvalue is 0.150619995805630402 Type 4: zero matrix Type 5: smallest eigenvalue is 0.783519984727020891 Type 6: smallest eigenvalue is 1.073366485789859492 Type 7: smallest eigenvalue is 0.487614639805665051 Written r.py Written qdashf.py \$ sage -python scripts/make_exact_qdash.py '5/18' --denominator 48 --dir output/ff84 --diagonalize Type 1: smallest eigenvalue is 0.826182425137056753 Type 2: smallest eigenvalue is 0.236313156340247743 Type 3: smallest eigenvalue is 0.152802778607211087 Type 4: zero matrix Type 5: smallest eigenvalue is 0.778791211059178923 Type 6: smallest eigenvalue is 1.024967451027120502 Type 7: smallest eigenvalue is 0.417055476220995869 Diagonalizing matrices... Written qdash.py Written r.py Added exact bound to flags.py \$ sage -python scripts/verify_bound.py --dir output/ff84 Written q.py Floating point bound (non-sharp graphs) is 0.273474365569272959 Exact bound (just sharp graphs) is 5/18 Bound (all graphs) is 5/18 \$ sage -python scripts/make_certificate.py --dir output/ff84 Written certificate to cert.js