\$ ./flagmatic --r 3 --n 5 --forbid-k4- --forbid 5:123124345 --dir output/cancel flagmatic version 1.5 ============================================================================ Forbidding 5:123124345 Forbidding 4.3 Using admissible graphs of order 5. Generated 1 type of order 1, with 2 flags of order 3. Generated 2 types of order 3, with [7, 4] flags of order 4. Generated 7 admissible graphs. Approximate floating-point bound is 0.22222222 \$ sage -python scripts/find_sharp_graphs.py --dir output/cancel Floating point bound is 0.222222222873386943. 3 members of H are sharp. 0.222222222873386943 : graph 1 (5:) 0.222222222726873864 : graph 5 (5:123124125) 0.222222222864505881 : graph 7 (5:123124135145) Written sharp graphs to flags.py \$ sage -python scripts/check_construction.py --n 5 --r 3 --vertex-transitive 3:123 Density is 2/9. 3 graphs of order 5 occur as induced subgraphs of the blow-up: 5: has density 31/81 (0.382716) 5:123124125 has density 20/81 (0.246914) 5:123124135145 has density 10/27 (0.370370) \$ sage -python scripts/make_zero_eigenvectors.py --vertex-transitive 3:123 --dir output/cancel Constructed 1 out of 1 zero eigenvectors for type 1. Constructed 4 out of 4 zero eigenvectors for type 2. Constructed 1 out of 1 zero eigenvectors for type 3. Written zev.py Written field to flags.py \$ sage -python scripts/factor_approximate_q.py --dir output/cancel Floating point bound is 0.222222222873386943. Type 1: smallest eigenvalue is 39.013830865958098570 Type 2: smallest eigenvalue is 0.326187267954483939 Type 3: smallest eigenvalue is 0.254045018768249420 Written r.py Written qdashf.py \$ sage -python scripts/make_exact_qdash.py '2/9' --denominator 4 --dir output/cancel --diagonalize Type 1: smallest eigenvalue is 39.013888888888885731 Type 2: smallest eigenvalue is 0.499999999999999667 Type 3: smallest eigenvalue is 0.250000000000000000 Diagonalizing matrices... Written qdash.py Written r.py Added exact bound to flags.py \$ sage -python scripts/verify_bound.py --dir output/cancel Written q.py Floating point bound (non-sharp graphs) is 0.172222222222222276 Exact bound (just sharp graphs) is 2/9 Bound (all graphs) is 2/9 \$ sage -python scripts/make_certificate.py --dir output/cancel Written certificate to cert.js