For fixed integers $k\ge3$ and $1\le d\le k-1$ and sufficiently large $n\in k\mathbb N$, we establish the sharp minimum $d$-degree thresholds that forces perfect matching in every $n$-vertex $k$-uniform hypergraphs. This was conjectued by Treglown and Zhao, and the $d=1$ case was conjectued by K\"uhn, Osthus and Treglo...
Jie Han, Hong-Liang Lu, Bin Wang et al.· 1 citation
A balanced $k$-partite $k$-graph is a $k$-uniform hypergraph whose vertex set is partitioned into $k$ classes of the same size and whose edges meet every class in exactly one vertex. Lo and Markstr\"om (2014) determined the minimum vertex-degree threshold for perfect matchings when $k=3$, and Lu, Wang and Yuan recently...
Jie Han, Hong-Liang Lu, Bin Wang et al.· 0 citations
Given a graph $F$, a family $\mathcal F$ of graphs on $[n]$ is \emph{$F$-intersecting} if $G\cap H$ contains a copy of $F$ for every $G,H\in\mathcal F$. We prove that there exists an absolute constant $\varepsilon>0$ such that every $P_4$-intersecting family $\mathcal F$ satisfies $|\mathcal F|\le\left(\frac12-\varepsi...
We show that optimally pseudorandom $K_4$-free graphs of order $n$ and degree $d = \Theta(n^{4/5})$ exist by constructing a graph in the split Cayley hexagon, matching the known upper bound. This resolves the first open case for $K_k$-free graphs after $k=3$ for which Alon gave a tight construction in 1994. This has a...
Jie Han, F. Ihringer, H. Van Maldeghem· 0 citations
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