Keevash, Lenz, and Mubayi proved a spectral Erd\H{o}s--Ko--Rado theorem, showing that, for sufficiently large $n$, the complete $t$-star uniquely maximizes the adjacency-tensor spectral radius among all $t$-intersecting $k$-uniform families. In this paper, we establish a spectral Hilton--Milner--Frankl theorem for nont...
Xu-Cheng Bu, Li-Hua Feng, Lu Lu et al.· 0 citations
A theorem of Li and Ning [Linear Algebra Appl. 515 (2017)] states that, for $n\geq4$, every balanced bipartite graph $G$ on $2n$ vertices with spectral radius $\lambda(G)\geq\sqrt{n(n-1)}$ contains a Hamilton path unless $G\simeq K_{n,n-1}\cup K_1$. Let $[n]=\{1,2,\ldots,n\}$. We prove a generalization of this theorem...
Xiao-Cong He, Rongrong Lu· Electronic Journal of Combin...· 1 citation
Let $k>t\ge 1$ be integers and set $d=k-t$. A $k$-uniform hypergraph $\mathcal F$ is called $t$-intersecting if any two edges intersect in at least $t$ vertices, and is called $t$-critical if its minimum $t$-transversal has size $k$. Frankl proved that, for $k\ge d^4$,$|\mathcal F|\le \binom{k+d}{d},$ with equality onl...
Lu Lu, Rongrong Lu, Qifan Wang et al.· 0 citations
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