Perfect tilings of 3-graphs with the generalised triangle

2025/05/08 by Candida Bowtell, Bowtell, Candida, Amarja Kathapurkar +5 · 2 citations
Engineering · Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Analysis and Transform Methods #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2505.05606

openalex publication_date 2025/05/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish a best-possible minimum codegree condition for the existence of a perfect tiling of a 3-uniform hypergraph H with copies of the generalised triangle T, which is the 3-uniform hypergraph with five vertices a, b, c, d, e and three edges abc, abd, cde. We also give an asymptotically-optimal minimum codegree condition for the rainbow version of the problem.

Citations

• Andrásfai--Erdős--Sós theorem for the generalized triangle
• Tiling dense hypergraphs
• The degree threshold for covering with all the connected 3-graphs with 3 edges
• The degree and codegree threshold for generalized triangle and some trees covering
• Codegree conditions for tiling complete k-partite k-graphs and loose cycles
• The complexity of perfect matchings and packings in dense hypergraphs
• Recent advances on Dirac-type problems for hypergraphs
• Mantel's Theorem for Random Hypergraphs
• Packing k-partite k-uniform hypergraphs
• Minimum codegree threshold for (K₄³-e)-factors
• Tiling 3-uniform hypergraphs with K₄³-2e
• Embedding large subgraphs into dense graphs
• Matching in hypergraphs of large minimum degree
• The minimum degree threshold for perfect graph packings
• On the Complexity of General Graph Factor Problems
• Degrees giving independent edges in a hypergraph
• The Factorization of Linear Graphs
• Paths, Trees, and Flowers
• Some Theorems on Abstract Graphs

Cited by

• Perfect tilings with the generalised triangle in k-graphs
• Positive codegree thresholds for perfect matchings in hypergraphs

Related

• Perfect tilings with the generalised triangle in k-graphs
• Codegree thresholds for covering 3-uniform hypergraphs
• Rainbow matchings for 3-uniform hypergraphs
• Minimum codegree threshold for C₆³-factors in 3-uniform Hypergraphs
• On Perfect Matchings and tilings in uniform Hypergraphs