k=3 c=1 a=1 n=9 w=7 m=2 (n-1)-(2k-1)m=-2 |E|=17 connected=True proper=True matching=4 edges  OK=True
k=3 c=2 a=3 n=20 w=16 m=4 (n-1)-(2k-1)m=-1 |E|=82 connected=True proper=True matching=9 edges  OK=True
k=3 c=3 a=6 n=36 w=29 m=7 (n-1)-(2k-1)m=0 |E|=263 connected=True proper=True matching=16 edges  OK=True
k=3 c=4 a=10 n=57 w=46 m=11 (n-1)-(2k-1)m=1 |E|=656 connected=True proper=True matching=25 edges  OK=True
k=3 c=5 a=15 n=83 w=67 m=16 (n-1)-(2k-1)m=2 |E|=1387 connected=True proper=True matching=36 edges  OK=True
k=3 c=6 a=21 n=114 w=92 m=22 (n-1)-(2k-1)m=3 |E|=2612 connected=True proper=True matching=49 edges  OK=True
k=3 c=7 a=28 n=150 w=121 m=29 (n-1)-(2k-1)m=4 |E|=4517 connected=True proper=True matching=64 edges  OK=True
k=4 c=1 a=1 n=13 w=11 m=2 (n-1)-(2k-1)m=-2 |E|=38 connected=True proper=True matching=6 edges  OK=True
k=4 c=2 a=3 n=28 w=24 m=4 (n-1)-(2k-1)m=-1 |E|=172 connected=True proper=True matching=13 edges  OK=True
k=4 c=3 a=6 n=50 w=43 m=7 (n-1)-(2k-1)m=0 |E|=543 connected=True proper=True matching=23 edges  OK=True
k=4 c=4 a=10 n=79 w=68 m=11 (n-1)-(2k-1)m=1 |E|=1349 connected=True proper=True matching=36 edges  OK=True
k=4 c=5 a=15 n=115 w=99 m=16 (n-1)-(2k-1)m=2 |E|=2851 connected=True proper=True matching=52 edges  OK=True
k=4 c=6 a=21 n=158 w=136 m=22 (n-1)-(2k-1)m=3 |E|=5373 connected=True proper=True matching=71 edges  OK=True
k=4 c=7 a=28 n=208 w=179 m=29 (n-1)-(2k-1)m=4 |E|=9302 connected=True proper=True matching=93 edges  OK=True
k=5 c=1 a=1 n=17 w=15 m=2 (n-1)-(2k-1)m=-2 |E|=67 connected=True proper=True matching=8 edges  OK=True
k=5 c=2 a=3 n=36 w=32 m=4 (n-1)-(2k-1)m=-1 |E|=294 connected=True proper=True matching=17 edges  OK=True
k=5 c=3 a=6 n=64 w=57 m=7 (n-1)-(2k-1)m=0 |E|=921 connected=True proper=True matching=30 edges  OK=True
k=5 c=4 a=10 n=101 w=90 m=11 (n-1)-(2k-1)m=1 |E|=2284 connected=True proper=True matching=47 edges  OK=True
k=5 c=5 a=15 n=147 w=131 m=16 (n-1)-(2k-1)m=2 |E|=4827 connected=True proper=True matching=68 edges  OK=True
k=5 c=6 a=21 n=202 w=180 m=22 (n-1)-(2k-1)m=3 |E|=9102 connected=True proper=True matching=93 edges  OK=True
k=5 c=7 a=28 n=266 w=237 m=29 (n-1)-(2k-1)m=4 |E|=15769 connected=True proper=True matching=122 edges  OK=True
k=6 c=1 a=1 n=21 w=19 m=2 (n-1)-(2k-1)m=-2 |E|=104 connected=True proper=True matching=10 edges  OK=True
k=6 c=2 a=3 n=44 w=40 m=4 (n-1)-(2k-1)m=-1 |E|=448 connected=True proper=True matching=21 edges  OK=True
k=6 c=3 a=6 n=78 w=71 m=7 (n-1)-(2k-1)m=0 |E|=1397 connected=True proper=True matching=37 edges  OK=True
k=6 c=4 a=10 n=123 w=112 m=11 (n-1)-(2k-1)m=1 |E|=3461 connected=True proper=True matching=58 edges  OK=True
k=6 c=5 a=15 n=179 w=163 m=16 (n-1)-(2k-1)m=2 |E|=7315 connected=True proper=True matching=84 edges  OK=True
k=6 c=6 a=21 n=246 w=224 m=22 (n-1)-(2k-1)m=3 |E|=13799 connected=True proper=True matching=115 edges  OK=True
k=6 c=7 a=28 n=324 w=295 m=29 (n-1)-(2k-1)m=4 |E|=23918 connected=True proper=True matching=151 edges  OK=True
k=7 c=1 a=1 n=25 w=23 m=2 (n-1)-(2k-1)m=-2 |E|=149 connected=True proper=True matching=12 edges  OK=True
k=7 c=2 a=3 n=52 w=48 m=4 (n-1)-(2k-1)m=-1 |E|=634 connected=True proper=True matching=25 edges  OK=True
k=7 c=3 a=6 n=92 w=85 m=7 (n-1)-(2k-1)m=0 |E|=1971 connected=True proper=True matching=44 edges  OK=True
k=7 c=4 a=10 n=145 w=134 m=11 (n-1)-(2k-1)m=1 |E|=4880 connected=True proper=True matching=69 edges  OK=True
k=7 c=5 a=15 n=211 w=195 m=16 (n-1)-(2k-1)m=2 |E|=10315 connected=True proper=True matching=100 edges  OK=True
k=7 c=6 a=21 n=290 w=268 m=22 (n-1)-(2k-1)m=3 |E|=19464 connected=True proper=True matching=137 edges  OK=True
k=7 c=7 a=28 n=382 w=353 m=29 (n-1)-(2k-1)m=4 |E|=33749 connected=True proper=True matching=180 edges  OK=True
Remark 3.3 graph: n=36 |E|=263 degrees 1..29 with 13 x8: True; identical to Definition-3.1 F_3^(3): True; colour class sizes (6, 13, 17), sum 36
exported ref_F3_c3_plusK1_n37.json: n=37, |E|=263
exported ref_F4_c3_plusK1_n51.json: n=51, |E|=543
exported ref_F5_c3_plusK1_n65.json: n=65, |E|=921
exported ref_F3_c4_n57.json: n=57, |E|=656
exported ref_F4_c4_n79.json: n=79, |E|=1349
exported ref_F3_c3_n36.json: n=36, |E|=263
k=3: argmin_c m/n over c<30 is c=5, m/n=0.192771 (16/(32k-13)=0.192771)
k=4: argmin_c m/n over c<30 is c=5, m/n=0.139130 (16/(32k-13)=0.139130)
k=10: argmin_c m/n over c<30 is c=5, m/n=0.052117 (16/(32k-13)=0.052117)
ALL CHECKS PASSED: True
