Spectrum and Combinatorics of Ramanujan Triangle Complexes
نویسنده
چکیده
Ramanujan graphs have extremal spectral properties, which imply a remarkable combinatorial behavior. In this paper we compute the high-dimensional Laplace spectrum of Ramanujan triangle complexes, and show that it implies a combinatorial expansion property, and a pseudo-randomness result. For this purpose we prove a Cheeger-type inequality and a mixing lemma of independent interest.
منابع مشابه
The spectrum of triangle-free regular graphs containing a cut vertex
We determine, for all n > 0, the set C(n) = {k: there exists a triangle-free k-regular graph on n vertices containing a cut vertex}.
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