Large Y_k,b -tilings and Hamilton ℓ -cycles in k-uniform hypergraphs

2021/08/28 by Luyining Gan, Gan, Luyining, Jie Han +5 · 1 citation
Mathematics · Computer Science · #Limits and Structures in Graph Theory #Advanced Graph Theory Research #Graph theory and applications

paper · pdf · doi:10.48550/arxiv.2109.00722

Abstract

Let Y_3,2 be the 3-uniform hypergraph with two edges intersecting in two vertices. Our main result is that any n-vertex 3-uniform hypergraph with at least \binomn3 - \binomn-m+13 + o(n³) edges contains a collection of m vertex-disjoint copies of Y_3,2, for m≤ n/7. The bound on the number of edges is asymptotically best possible. This problem generalizes the Matching Conjecture of Erdős. We then use this result combined with the absorbing method to determine the asymptotically best possible minimum (k-3)-degree threshold for ℓ-Hamiltonicity in k-graphs, where k≥ 7 is odd and ℓ=(k-1)/2. Moreover, we give related results on Y_k,b -tilings and Hamilton ℓ -cycles with d -degree for some other values of k,ℓ,d .

Citations

• Some Theorems on Abstract Graphs
• Degrees giving independent edges in a hypergraph

Cited by

• Loose Hamiltonicity

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