Codegree Conditions for Tiling Complete k-Partite k-Graphs and Loose Cycles

Autor(es)

Gao, Wei ^[1] ; Han, Jie ^[2] ; Zhao, Yi ^[3]

Afiliação do(s) autor(es)

^[1] Auburn Univ, Dept Math & Stat, Auburn, AL 36830 - USA

^[2] Univ Rhode Isl, Dept Math, 5 Lippitt Rd, Kingston, RI 02881 - USA

^[3] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 - USA

• Tipo de documento: Artigo Científico
• Fonte: COMBINATORICS PROBABILITY & COMPUTING; v. 28, n. 6, p. 840-870, NOV 2019.
• Citações Web of Science: 1

Resumo

Given two k-graphs (k-uniform hypergraphs) F and H, a perfect F-tiling (or F-factor) in H is a set of vertex-disjoint copies of F that together cover the vertex set of H. For all complete k-partite k-graphs K, Mycroft proved a minimum codegree condition that guarantees a K-factor in an n-vertex k-graph, which is tight up to an error term o(n). In this paper we improve the error term in Mycroft's result to a sublinear term that relates to the Turan number of K when the differences of the sizes of the vertex classes of K are co-prime. Furthermore, we find a construction which shows that our improved codegree condition is asymptotically tight in infinitely many cases, thus disproving a conjecture of Mycroft. Finally, we determine exact minimum codegree conditions for tiling K-(k)(1, . . . , 1, 2) and tiling loose cycles, thus generalizing the results of Czygrinow, DeBiasio and Nagle, and of Czygrinow, respectively. (AU)

• Processo FAPESP: 14/18641-5 - Circuitos hamiltonianos e problemas de ladrilhamento em hipergrafos
• Beneficiário: Jie Han
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado
• Processo FAPESP: 15/07869-8 - Emparelhamento perfeitos e ladrilhamentos em hipergrafos
• Beneficiário: Jie Han
• Modalidade de apoio: Bolsas no Exterior - Estágio de Pesquisa - Pós-Doutorado
• Processo FAPESP: 13/03447-6 - Estruturas combinatórias, otimização e algoritmos em Teoria da Computação
• Beneficiário: Carlos Eduardo Ferreira
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