2023/08/19 by Yue Ma, Xinmin Hou, Ma, Yue +3 · 1 citation
Computer Science · Mathematics · #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph theory and applications #Limits and Structures in Graph Theory
paper · pdf · doi:10.48550/arxiv.2308.10059
openalex publication_date 2023/08/19 · openalex created_date 2023/08/23 · openalex updated_date 2026/07/28
Given two r-uniform hypergraphs F and H, we say that H has an F-covering if every vertex in H is contained in a copy of F. Let ci(n,F) be the least integer such that every n-vertex r-graph H with δi(H)>ci(n,F) has an F-covering. Falgas-Ravry, Markstöm and Zhao (Combin. Probab. Comput., 2021) asymptotically determined c1(n,K4(3)-), where K4(3)- is obtained by deleting an edge from the complete 3-graph on 4 vertices. Later, Tang, Ma and Hou (arXiv, 2022) asymptotically determined c1(n,C6(3)), where C6(3) is the linear triangle, i.e. C6(3)=([6],\123,345,561\). In this paper, we determine c1(n,F5) asymptotically, where F5 is the generalized triangle, i.e. F5=([5],\123,124,345\). We also determine the exact values of c1(n,F), where F is any connected 3-graphs with 3 edges and F∉\K4(3)-, C6(3), F5\.