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Sign inarXiv:2607.11726 combines core and truss reductions with the Lovász theta function and reports a certified integer upper bound of 168 for C2000.9, improving the previous 177, plus improvements for C500.9 (83 to 73) and C1000.9 (122 to 115). The exact clique numbers of these three graphs remain unknown.
Version 1 posted 13 July 2026 as an arXiv preprint; no refereed publication or independent recomputation is recorded.
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Run the reductions and the theta-function bound on the DIMACS instance file and compare.
Soundness of the new reduction notions and of the claim that the bound is certified.
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