A graph $H$ is $K_{r+1}$-Tur\'an-good if, for every sufficiently large $n$, the Tur\'an graph $T_r(n)$ maximizes the number of copies of $H$ among all $n$-vertex $K_{r+1}$-free graphs, and it is strictly $K_{r+1}$-Tur\'an-good when this extremal graph is unique. Morrison, Nir, Norin, Rz\k{a}\.zewski and Wesolek proved...
A graph $H$ is $K_{r+1}$-Tur\'an-good if, for every sufficiently large $n$, the Tur\'an graph $T_r(n)$ maximizes the number of copies of $H$ among all $n$-vertex $K_{r+1}$-free graphs. It is strictly $K_{r+1}$-Tur\'an-good if $T_r(n)$ is the unique extremal graph. Morrison, Nir, Norin, Rz\k{a}\.zewski and Wesolek [\emp...
Let $\rho(n,d)$ denote the maximum adjacency spectral radius among all connected nonregular graphs of order $n$ and maximum degree $d$. A graph attaining this maximum is called an extremal graph. Liu [J. Combin. Theory Ser. B, 2024] determined the extremal graphs for $d=3,4$ and formulated two conjectures for general $...
The Erd\H{o}s Matching Conjecture concerns the maximum number of hyperedges in an $r$-uniform hypergraph with bounded matching number. In this paper, we study a spectral counterpart of this conjecture. For sufficiently large $n$, we determine the maximum spectral radius over all $n$-vertex $r$-uniform hypergraphs whose...
Liying Kang, Yongchun Lu, Xiying Yuan et al.· 2 citations
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