Programs and data for "A thrackle on n vertices has fewer than 4n/3 edges"
Tejasvi Singh Tomar · Zenodo (CERN European Organization for Nuclear Research) · 2026
Programs, input graphs, filter lists, split states and logs for the paper A thrackle on n vertices has fewer than 51n/38 edges (doi:10.5281/zenodo.23549049). The paper proves that every thrackle with n ≥ 4 vertices has at most 51(n − 1)/38 edges. The computations show that the dumbbells DB(6, 8, −1), DB(6, 8, −2) and DB(6, 8, −3) are not thrackleable, settle the cases covered by three enumerations (a 6-cycle and an 8-cycle with a common edge; two 6-cycles with a common vertex; closed walks of length 10 along a run of edges of a 6-cycle), and check the programs on graphs with known answers. Files. thrackle-bound-7565e05d2787.zip (identical to the GitHub repository github.com/tejasvi/thrackle-bound at commit 7565e05d2787e9b935e3550c73d56b533c3fe11d): the search program src/thr2.c with the left-right planarity test src/lr.c, the enumeration and helper scripts, the input graphs, the filter lists and split states (the 694,211 states of the main run, compressed), the logs of all runs (576 parts for DB(6, 8, −1), 96 for DB(6, 8, −2)), the static binaries used for the large runs with their sources and build commands, the data from comparing the planarity test with an implementation of the algorithm of Demoucron, Malgrange and Pertuiset, and, in independent/, the second implementation of the search and of the enumerations (Section 5.4 of the paper) with the outputs of its runs. SHA256SUMS: checksums of the files in this record. Reproducing. The search program builds with gcc -O2 -o thr2 src/thr2.c src/lr.c. The README lists the commands that produced every file. The counts and small cases take seconds, DB(6, 8, −2) about 36 thread-hours, and DB(6, 8, −1) about 2,160 thread-hours, split into 576 independent parts. The enumerations need Python 3.