Extremal Uncrowded Hypergraphs

Abstract Let G be a (k + 1)-graph (a hypergraph with each hyperedge of size k + 1) with n vertices and average degreee t. Assume k ⪡ t ⪡ n. If G is uncrowded (contains no cycle of size 2, 3, or 4) then there exists and independent set of size c k ( n t )( ln t) 1 k .

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