The Hypergraph Turán Densities of Tight Cycles Minus an Edge

Bernard Lidický, Connor Mattes Florian Pfender

This page is containing computer assisted parts of the paper titled The Hypergraph Turán Densities of Tight Cycles Minus an Edge A preliminary version of the paper can be downloaded here.

You can download the technical things as one archive

• anc_C5-.tar.gz (7.3GB, unpacked 37GB)

Description of the files in anc_C5-.tar.gz Below is old copy.

• check.sh ... small bash script that reads log from rounding and prints the results
• check_full.sh ... small bash script that does rounding using SageMath
• rounding_Integer.sage ... SageMath tools for rounding semidefinite program
• a.out ... the program creating semidefinite program
• F_edges*__forbidden.txt ... list of forbidden (induced) subgraphs
• F_edges*__nX_labeled.txt ... list of labeled graphs on X vertices used in the calculation (generated)
• F_edges*__nX_unlabeled.txt ... list of all graphs on up to X vertices (generated)
• F_edges*__objective*.txt ... Function to optimize
• SDP_nX_?B_F_*edges*__objective.txt.dat-s ... semidefinite program - input to csdp(generated)
• SDP_nX_?B_F_*edges*__objective.txt.dat-s.result ... numerical solution from csdp (generated)
• SDP_nX_?B_F_*edges*__objective.txt.dat-s.result.rounded.... ... rational solution from numerical one by SageMath (generated)
• SDP_nX_LB_F_*edges*__objective.txt.dat-s.csdp.log ... csdp solver output (generated)
• round* ... scrips and outputs for rounding the semidefinite program.

Checking Claim15/
Lowest 5  coefficients, Claim 15 needs them to be >= 0
2  6 0   1 1 2 2 3 3   6 123 124 125 136 146 156   # 2
1  6 0   1 1 2 2 3 3   7 124 125 134 135 146 156 236   # 32
0  6 0   1 1 2 2 3 3   8 135 136 145 146 235 236 245 246   # 430
0  6 0   1 1 2 2 3 3   7 125 126 134 235 236 245 246   # 254
0  6 0   1 1 2 2 3 3   7 123 124 135 136 145 146 256   # 6

Checking Claim16/
x_3 >= 
28573510621292340416114469021662641717220315285760 / 90000000000000000000000000000000000000000000000000  # =  0.3174834513476927

x_2x_3 >= 
9559626899090265624635277953041184351826677518080 / 90000000000000000000000000000000000000000000000000  # =  0.10621807665655851

x_1 <= 
30449168515566516705988894884018810403840868532480 / 90000000000000000000000000000000000000000000000000  # =  0.3383240946174057

x_1x_2 <= 
10228802399636656346745151315896170937104806321920 / 90000000000000000000000000000000000000000000000000  # =  0.11365335999596285


Checking Claim17/
f1 - f2 + 3/4(t^2-t^3) <= 
2708550505765237186152349931805876557412026112 / 9000000000000000000000000000000000000000000000000  # =  0.00030095005619613745

Checking Claim18/
AB >=  (be patient)
6992563964043144671187403879359734580164933116416 / 36000000000000000000000000000000000000000000000000  # =  0.19423788789008734

Checking Claim20/
f2 <=  (be more patient)
513942694525534071813209615184221513859091135488 / 36000000000000000000000000000000000000000000000000  # =  0.014276185959042613

Checking Lemma10/
K_2 <=  
14012179180700882058867945296422074007373856 / 56000000000000000000000000000000000000000000  # =  0.2502174853696586

Checking Lemma12/
6/15 H_6 + 0.196/4 H_3^T + 0.366/10 H_4^T >= 
72020832762027961128341863739816262583738772820000 / 1302840000000000000000000000000000000000000000000000  # =  0.055279875320091466