High-dimensional Hoffman bound and extremal combinatorics

Yuval Filmus, Konstantin Golubev and Noam Lifshitz
Alg. Comb.

We generalize the Hoffman bound to simplicial complexes. We demonstrate our result by giving spectral proofs for Mantel’s theorem and for an optimal bound on $s$-wise intersecting families due to Frankl and Tokushige. As a new application, we give tight bounds on a question of Frankl about hypergraphs without extended triangles.


 author = {Yuval Filmus and Konstantin Golubev and Noam Lifshitz},
 title = {High dimensional {H}offman bound and applications in extremal combinatorics},
 journal = {Algebraic Combinatorics},
 volume = {4},
 number = {6},
 pages = {1005--1026},
 year = {2021}
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