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摘要
Given positive integers a <= b <= c, let K-a,K-b,K-c be the complete 3-partite 3-uniform hypergraph with three parts of sizes a,b,c. Let H be a 3-uniform hypergraph on n vertices where n is divisible by a+b+c. We asymptotically determine the minimum vertex degree of H that guarantees a perfect K-a,K-b,K-c-tiling, that is, a spanning subgraph of H consisting of vertex-disjoint copies of K-a,K-b,K-c. This partially answers a question of Mycroft, who proved an analogous result with respect to codegree for r-uniform hypergraphs for all r >= 3. Our proof uses a lattice-based absorbing method, the concept of fractional tiling, and a recent result on shadows for 3-graphs.
- 出版日期2017-7
