$ ./flagmatic --r 3 --n 6 --forbid 5.10 --forbid-induced 5.8 --dir output/k58i flagmatic version 1.5 ============================================================================ Forbidding 5.10 Forbidding 5.8 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 12 flags of order 4. Generated 5 types of order 4, with [64, 64, 63, 58, 48] flags of order 5. Generated 1681 admissible graphs. Approximate floating-point bound is 0.75000000 $ sage -python scripts/find_sharp_graphs.py --dir output/k58i Floating point bound is 0.750000000026281199. 4 members of H are sharp. 0.749999999946320273 : graph 1 (6:) 0.750000000017899682 : graph 883 (6:123124125126134135136145146156) 0.750000000026281199 : graph 1679 (6:123124125126134135136145146156234235236245246256) 0.750000000023835489 : graph 1681 (6:123124125126134135136145146235236245246256345346356456) Written sharp graphs to flags.py $ sage -python scripts/check_construction.py --n 6 --r 3 --vertex-transitive 2:112122 Density is 3/4. 4 graphs of order 6 occur as induced subgraphs of the blow-up: 6: has density 1/32 (0.031250) 6:123124125126134135136145146156 has density 3/16 (0.187500) 6:123124125126134135136145146156234235236245246256 has density 15/32 (0.468750) 6:123124125126134135136145146235236245246256345346356456 has density 5/16 (0.312500) $ sage -python scripts/make_zero_eigenvectors.py --vertex-transitive 2:112122 --dir output/k58i Constructed 1 out of 1 zero eigenvectors for type 1. Constructed 2 out of 2 zero eigenvectors for type 2. Constructed 1 out of 1 zero eigenvectors for type 3. Constructed 0 out of 0 zero eigenvectors for type 4. Constructed 0 out of 0 zero eigenvectors for type 5. Constructed 1 out of 1 zero eigenvectors for type 6. Constructed 3 out of 3 zero eigenvectors for type 7. Written zev.py Written field to flags.py $ sage -python scripts/factor_approximate_q.py --dir output/k58i Floating point bound is 0.750000000026281088. Type 1: smallest eigenvalue is 0.122294107076181380 Type 2: smallest eigenvalue is 0.015024677400633084 Type 3: smallest eigenvalue is 0.187012249411191989 Type 4: smallest eigenvalue is 0.193723924200698339 Type 5: smallest eigenvalue is 0.104699440334252020 Type 6: smallest eigenvalue is 0.138098740999838487 Type 7: smallest eigenvalue is 0.157257064915669875 Written r.py Written qdashf.py $ sage -python scripts/make_exact_qdash.py '3/4' --denominator 72 --dir output/k58i --diagonalize Type 1: smallest eigenvalue is 0.116134691733427484 Type 2: smallest eigenvalue is 0.012992904603151672 Type 3: smallest eigenvalue is 0.208333333333333315 Type 4: smallest eigenvalue is 0.195803985658467961 Type 5: smallest eigenvalue is 0.109455249673480803 Type 6: smallest eigenvalue is 0.109940477176479298 Type 7: smallest eigenvalue is 0.174802589411484799 Diagonalizing matrices... Written qdash.py Written r.py Added exact bound to flags.py $ sage -python scripts/verify_bound.py --dir output/k58i Written q.py Floating point bound (non-sharp graphs) is 0.744213425241069371 Exact bound (just sharp graphs) is 3/4 Bound (all graphs) is 3/4 $ sage -python scripts/make_certificate.py --dir output/k58i Written certificate to cert.js