\$ ./flagmatic --n 6 --r 3 --induced-density 4.3 --forbid-k4 --dir output/k4max43 flagmatic version 1.5 ============================================================================ Optimizing for density of 4.3. Forbidding 4.4 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 11 flags of order 4. Generated 4 types of order 4, with [64, 56, 50, 45] flags of order 5. Generated 964 admissible graphs. Approximate floating-point bound is 0.59259259 \$ sage -python scripts/find_sharp_graphs.py --dir output/k4max43 Floating point bound is 0.592592592748368285. 8 members of H are sharp. 0.592592592482279912 : graph 1 (6:) 0.592592592643053195 : graph 13 (6:123124125126) 0.592592592677961050 : graph 677 (6:123124125136146156236246256) 0.592592592725136313 : graph 681 (6:123124125126134135136145146156) 0.592592592748368285 : graph 925 (6:123124125126134135136145146256356456) 0.592592592643013893 : graph 944 (6:123124125134135145236246256346356456) 0.592592592748062419 : graph 958 (6:123124125126134135136245246256345346356) 0.592592592713214295 : graph 964 (6:123124125134135146156236245246256345346356) Written sharp graphs to flags.py \$ sage -python scripts/check_construction.py --n 6 --r 3 --induced-density 4.3 --vertex-transitive 3:112223331123 Density of 4.3 is 16/27. 8 graphs of order 6 occur as induced subgraphs of the blow-up: 6: has density 7/243 (0.028807) 6:123124125126 has density 5/81 (0.061728) 6:123124125136146156236246256 has density 20/243 (0.082305) 6:123124125126134135136145146156 has density 4/27 (0.148148) 6:123124125134135145236246256346356456 has density 5/81 (0.061728) 6:123124125126134135136145146256356456 has density 20/81 (0.246914) 6:123124125126134135136245246256345346356 has density 20/81 (0.246914) 6:123124125134135146156236245246256345346356 has density 10/81 (0.123457) \$ sage -python scripts/make_zero_eigenvectors.py --vertex-transitive 3:112223331123 --dir output/k4max43 Constructed 1 out of 1 zero eigenvectors for type 1. Constructed 3 out of 3 zero eigenvectors for type 2. Constructed 5 out of 5 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 4 out of 4 zero eigenvectors for type 6. Written zev.py Written field to flags.py \$ sage -python scripts/factor_approximate_q.py --dir output/k4max43 Floating point bound is 0.592592592748368285. Type 1: smallest eigenvalue is 0.188462452037512385 Type 2: smallest eigenvalue is 0.047590115926319641 Type 3: smallest eigenvalue is 0.127354977745658432 Type 4: smallest eigenvalue is 0.119952354146454665 Type 5: smallest eigenvalue is 0.099066496171228979 Type 6: smallest eigenvalue is 0.134182269813466037 Written r.py Written qdashf.py \$ sage -python scripts/make_exact_qdash.py '16/27' --denominator 120 --dir output/k4max43 --diagonalize Type 1: smallest eigenvalue is 0.187683599189045730 Type 2: smallest eigenvalue is 0.040659093110981398 Type 3: smallest eigenvalue is 0.134400060634046581 Type 4: smallest eigenvalue is 0.114867726450753854 Type 5: smallest eigenvalue is 0.058596934908722281 Type 6: smallest eigenvalue is 0.136652875970569548 Diagonalizing matrices... Written qdash.py Written r.py Added exact bound to flags.py \$ sage -python scripts/verify_bound.py --dir output/k4max43 Written q.py Floating point bound (non-sharp graphs) is 0.591159152281030331 Exact bound (just sharp graphs) is 16/27 Bound (all graphs) is 16/27 \$ sage -python scripts/make_certificate.py --dir output/k4max43 Written certificate to cert.js