Minimum vertex degree thresholds for tiling complete 3-partite 3-graphs

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:149

Article

Han, Jie¹  Zang, Chuanyun²  Zhao, Yi² 

[1] Univ Sao Paulo, Inst Matemat & Estat, Rua Matao 1010, BR-05508090 Sao Paulo, Brazil

[2] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA

关键词: Graph packing;    Hypergraph;    Absorbing method;    Regularity lemma;   

DOI  :  10.1016/j.jcta.2017.02.003

来源: Elsevier

【 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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free