$ ./flagmatic --r 3 --n 6 --forbid-f32 --forbid-induced 4.3 --dir output/43if32 flagmatic version 1.5 ============================================================================ Forbidding 5:123124125345 Forbidding 4.3 as an induced subgraph. Using admissible graphs of order 6. Generated 1 type of order 0, with 2 flags of order 3. Generated 1 type of order 2, with 9 flags of order 4. Generated 4 types of order 4, with [41, 29, 20, 11] flags of order 5. Generated 122 admissible graphs. Approximate floating-point bound is 0.37500000 $ sage -python scripts/find_sharp_graphs.py --dir output/43if32 Floating point bound is 0.375000001387706672. 6 members of H are sharp. 0.375000000696310842 : graph 1 (6:) 0.375000000654722720 : graph 12 (6:123124125126) 0.375000001387706672 : graph 55 (6:123124125136146156) 0.375000000654717891 : graph 109 (6:123124135145236246356456) 0.375000000899048114 : graph 118 (6:123124125126134135136234235236) 0.375000001306261543 : graph 122 (6:123124125126134135146156234235246256) Written sharp graphs to flags.py $ sage -python scripts/check_construction.py --n 6 --r 3 --vertex-transitive 4:123124134234 Density is 3/8. 6 graphs of order 6 occur as induced subgraphs of the blow-up: 6: has density 47/512 (0.091797) 6:123124125126 has density 45/512 (0.087891) 6:123124125136146156 has density 45/128 (0.351562) 6:123124135145236246356456 has density 45/512 (0.087891) 6:123124125126134135136234235236 has density 15/128 (0.117188) 6:123124125126134135146156234235246256 has density 135/512 (0.263672) $ sage -python scripts/make_zero_eigenvectors.py --vertex-transitive 4:123124134234 --dir output/43if32 Constructed 1 out of 1 zero eigenvectors for type 1. Constructed 2 out of 2 zero eigenvectors for type 2. Constructed 8 out of 8 zero eigenvectors for type 3. Constructed 0 out of 0 zero eigenvectors for type 4. Constructed 1 out of 1 zero eigenvectors for type 5. Constructed 1 out of 1 zero eigenvectors for type 6. Written zev.py Written field to flags.py $ sage -python scripts/factor_approximate_q.py --dir output/43if32 Floating point bound is 0.375000001387706672. Type 1: smallest eigenvalue is 0.711044358923371034 Type 2: smallest eigenvalue is 0.006664690837344357 Type 3: smallest eigenvalue is 0.125207622301134913 Type 4: smallest eigenvalue is 0.091651093300419317 Type 5: smallest eigenvalue is 0.087193811911567359 Type 6: smallest eigenvalue is 0.093750031790476251 Written r.py Written qdashf.py $ sage -python scripts/make_exact_qdash.py '3/8' --denominator 240 --dir output/43if32 --diagonalize Type 1: smallest eigenvalue is 0.709409238941881570 Type 2: smallest eigenvalue is 0.005247266118908665 Type 3: smallest eigenvalue is 0.130062764363572059 Type 4: smallest eigenvalue is 0.092486766699905798 Type 5: smallest eigenvalue is 0.090281388988065286 Type 6: smallest eigenvalue is 0.087809493407926986 Diagonalizing matrices... Written qdash.py Written r.py Added exact bound to flags.py $ sage -python scripts/verify_bound.py --dir output/43if32 Written q.py Floating point bound (non-sharp graphs) is 0.372241650035191607 Exact bound (just sharp graphs) is 3/8 Bound (all graphs) is 3/8 $ sage -python scripts/make_certificate.py --dir output/43if32 Written certificate to cert.js