Table 11: Comparison of formulations 𝐸 𝐶 𝑡 and 𝐷 𝐶 𝑢 𝑡 𝑡 with and without using odd hole ienqualities. Index 𝑜 denotes if odd hole inequalities are separated, index 𝑏 indicates that odd hole inequalities have been used to induce branching over related label variables.

E C t n / D C u t t n E C t n o / D C u t t n o E C t n o b / D C u t t n o b
| 𝑉 | , | 𝐸 | , 𝑎 , | 𝐿 | cnt opt obj 𝑡 bbn cuts opt obj 𝑡 bbn cuts oh opt obj 𝑡 bbn cuts oh

1 0 0 , 2 4 7 , 1 , 6 1 10 10 19.6 14 4944 4486 10 19.6 25 5692 5141 23 10 19.6 17 5226 4701 19
10 10 19.6 12 1148 759 10 19.6 13 1163 772 1 10 19.6 13 1121 733 1
1 0 0 , 2 4 7 , 1 , 1 8 5 10 2 51.2 5760 163875 182801 2 51.2 5760 144151 159964 194 2 51.1 5760 143562 159321 173
10 6 49.8 3195 87152 60318 6 49.8 3214 83347 58322 11 6 49.8 3197 85997 60585 13
1 0 0 , 9 0 0 , 1 , 2 4 7 10 10 14.8 344 36386 16745 10 14.8 417 37993 18284 134 10 14.8 343 34639 15817 120
10 10 14.8 835 13677 8698 10 14.8 892 14659 9364 1 10 14.8 987 15816 10131 2
1 0 0 , 9 0 0 , 1 , 7 4 2 10 2 37.1 6450 120465 121687 3 36.8 6377 126819 128924 1251 2 36.7 6007 119218 119667 1308
10 7 35.8 2432 36099 27852 7 35.8 2369 34717 26348 77 7 35.8 2371 33757 26083 61
1 0 0 , 2 4 7 5 , 1 , 6 1 8 10 8 13.2 1400 34106 18769 8 13.3 2499 48599 28883 174 8 13.3 1820 35479 21775 138
10 5 13.5 4557 9195 8543 7 13.5 4261 8305 7615 9 7 13.3 4318 8322 7769 8
1 0 0 , 2 4 7 5 , 1 , 1 8 5 6 10 4 31.0 5038 59605 57375 5 30.8 4133 53079 52191 709 4 31.0 4499 54945 54254 614
10 7 30.2 3552 12337 97809 30.0 2827 8780 6809 51 9 30.0 2778 8061 6898 39

1 0 0 , 2 4 7 , 2 , 6 1 10 10 16.6 12 4707 4080 10 16.6 14 5148 4496 23 10 16.6 13 4987 4363 20
10 10 16.6 16 1162 787 10 16.6 17 1161 788 0 10 16.6 16 1146 775 1
1 0 0 , 2 4 7 , 2 , 1 8 5 10 7 35.0 2375 102179 93532 6 35.1 3485 137028 125999 272 7 35.0 2431 102595 90520 178
10 10 34.7 61 4661 369610 34.7 69 5073 4081 8 10 34.7 22 1758 1630 4
1 0 0 , 9 0 0 , 2 , 2 4 7 10 10 11.9 629 42052 20637 9 12.0 997 48954 22866 137 10 11.9 857 41933 21903 129
10 10 11.9 681 5906 5180 10 11.9 891 8242 6868 6 10 11.9 1000 8936 7734 11
1 0 0 , 9 0 0 , 2 , 7 4 2 10 3 26.3 5242 119550 107358 3 26.2 5395 118483 104341 1312 4 26.3 4841 107072 94593 1220
10 9 25.6 1489 24931 17663 9 25.6 1603 24112 18031 82 9 25.6 1443 23837 16801 67
1 0 0 , 2 4 7 5 , 2 , 6 1 8 10 10 10.9 506 22467 6432 10 10.9 748 28917 9107 44 10 10.9 388 17770 3684 14
10 5 11.2 5664 11813 9786 5 11.2 5736 10958 9467 7 6 11.1 5727 11155 9316 8
1 0 0 , 2 4 7 5 , 2 , 1 8 5 6 10 4 23.2 5213 61908 532941 23.8 6490 74525 64822 822 2 23.5 6298 72256 62059 754
10 5 22.8 4259 8850 8481 7 22.6 3642 7480 7073 22 8 22.5 3479 7831 7173 20

1 0 0 , 2 4 7 , 5 , 6 1 10 10 10.5 0 306 359 10 10.5 0 306 359 1 10 10.5 1 267 338 1
10 10 10.5 5 115 134 10 10.5 5 115 134 0 10 10.5 5 115 134 0
1 0 0 , 2 4 7 , 5 , 1 8 5 10 6 20.6 3467 143690 125295 4 20.7 4461 157779 137051 937 6 20.6 3047 116829 103068 673
10 10 20.5 698 45870 25073 9 20.5 787 43883 24921 12 9 20.5 783 45144 25575 10
1 0 0 , 9 0 0 , 5 , 2 4 7 10 10 7.8 128 12441 651 10 7.8 134 12521 631 2 10 7.8 157 13710 862 3
10 10 7.8 1628 15222 9552 10 7.8 1513 15071 9222 1 10 7.8 1540 15153 9365 0
1 0 0 , 9 0 0 , 5 , 7 4 2 10 3 15.1 5140 139983 90176 4 15.0 4838 132756 83094 702 4 15.0 4458 125665 78327 651
10 6 14.8 4406 44628 32312 5 14.9 4520 45818 33172 22 5 14.9 4392 44435 32267 18
1 0 0 , 2 4 7 5 , 5 , 6 1 8 10 10 6.9 255 6604 532 10 6.9 253 6581 519 0 10 6.9 262 6701 577 0
10 6 7.1 5089 5318 3529 6 7.0 5092 5503 3685 0 6 7.0 5093 5447 3608 0
1 0 0 , 2 4 7 5 , 5 , 1 8 5 6 10 6 13.0 3472 72582 38165 7 12.9 3132 62473 33275 255 7 12.9 2343 50106 24087 158
10 4 13.1 5743 7934 7389 3 13.3 6505 8896 8420 9 3 13.1 6213 8259 7770 8

1 0 × 1 0 , 3 6 0 , 1 , 3 0 10 10 9.2 4 1639 1544 10 9.2 5 1427 1350 10 10 9.2 5 1427 1384 11
10 10 9.2 34 1892 1710 10 9.2 32 1685 1510 5 10 9.2 34 1711 1576 6
1 0 × 1 0 , 3 6 0 , 1 , 5 0 9 8 13.0 1578 83996 67834 8 13.0 1550 81112 66089 310 9 12.9 619 54900 42488 145
9 9 12.9 302 20596 12907 9 12.9 387 25142 16180 23 9 12.9 298 19938 12261 8
1 0 × 1 0 , 3 6 0 , 1 , 8 0 10 0 19.6 7200 229619 202787 0 19.8 7200 211903 186885 1086 0 19.5 7200 211561 188812 1102
10 0 18.7 7200 283625 220940 0 18.8 7200 232626 190432 403 0 19.0 7200 223970 188832 381

2 0 × 2 0 , 1 5 2 0 , 1 , 3 0 10 10 11.5 91 3757 423110 11.5 107 3749 43100 10 11.5 106 3799 4249 0
10 10 11.5 627 4058 10961 10 11.5 753 4028 11567 0 10 11.5 705 4112 112610
2 0 × 2 0 , 1 5 2 0 , 1 , 5 0 10 10 17.0 3834 212265 107170 9 17.0 4232 209923 10575532 9 17.0 4324 210003 107385 39
10 0 17.0 7200 86172 64236 0 17.0 7200 77221 60603 6 0 17.0 7200 80453 59244 4
2 0 × 2 0 , 1 5 2 0 , 1 , 8 0 10 0 24.8 7200 146616 112030 0 24.8 7200 133250 102086 626 0 24.9 7200 131641 101479577
10 0 25.2 7200 43604 447550 25.2 7200 39262 41704 21 0 25.2 7200 39451 4295219