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We prove that the vertex degree threshold for tiling (the 3‐uniform hypergraph with four vertices and two triples) in a 3‐uniform hypergraph on vertices is , where if and otherwise. This result is best possible, and is one of the first results on vertex degree conditions for hypergraph tiling.
Given a bipartite graph H and a positive integer n such that v(H) divides 2n, we define the minimum degree threshold for bipartite H‐tiling, δ2(n, H), as the smallest integer k such that every bipartite graph G with n vertices in each partition and minimum degree δ(G)≥k contains a spanning subgraph consisting of vertex‐disjoint copies of H. Zhao, Hladký‐Schacht, Czygrinow‐DeBiasio determined δ2(n, K...
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