TY - JOUR
T1 - Minimum vertex degree thresholds for tiling complete 3-partite 3-graphs
AU - Han, Jie
AU - Zang, Chuanyun
AU - Zhao, Yi
N1 - Publisher Copyright:
© 2017 Elsevier Inc.
PY - 2017/7/1
Y1 - 2017/7/1
N2 - Given positive integers a≤b≤c, let Ka,b,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 Ka,b,c-tiling, that is, a spanning subgraph of H consisting of vertex-disjoint copies of Ka,b,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.
AB - Given positive integers a≤b≤c, let Ka,b,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 Ka,b,c-tiling, that is, a spanning subgraph of H consisting of vertex-disjoint copies of Ka,b,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.
KW - Absorbing method
KW - Graph packing
KW - Hypergraph
KW - Regularity lemma
UR - http://www.scopus.com/inward/record.url?scp=85013777675&partnerID=8YFLogxK
U2 - 10.1016/j.jcta.2017.02.003
DO - 10.1016/j.jcta.2017.02.003
M3 - Article
AN - SCOPUS:85013777675
SN - 0097-3165
VL - 149
SP - 115
EP - 147
JO - Journal of Combinatorial Theory. Series A
JF - Journal of Combinatorial Theory. Series A
ER -