Large edge up-Laplacian spectral gaps in triangle families force minimum degree at least ceil(lambda)-1 and identify complete n-cliques as the only maximizers at size binom(n,3), with the max-gap function non-monotone between clique thresholds.
The theta number of simpli- cial complexes
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Triangle Families with Large Edge Up-Laplacian Spectral Gap
Large edge up-Laplacian spectral gaps in triangle families force minimum degree at least ceil(lambda)-1 and identify complete n-cliques as the only maximizers at size binom(n,3), with the max-gap function non-monotone between clique thresholds.