For a $3$-uniform hypergraph $H$, let $\sigma(H)$ be the minimum over the vertices of $H$ of the spectral radius of the link. Lin, Lu, Yuan and Zhao conjectured that $\sigma(H)>\tfrac{2n}3-2$ forces a perfect matching in a $3$-graph of order $n$ divisible by three, and Lu and Yuan conjectured that $\sigma(H)>\tau(q)$ f...
For a $k$-uniform hypergraph $\mathcal H$, the shadow of $\mathcal H$ is the graph whose edges are the pairs covered by a hyperedge. In this paper, for all sufficiently large $n$, we determine the $n$-vertex $k$-uniform hypergraphs of maximum adjacency-tensor spectral radius whose shadow has no $K_t$ minor, for every $...
For an integer $k\ge3$, a $k$-angulation is a simple $2$-connected outerplane graph whose interior faces are bounded by $k$-cycles, and a closed $k$-angulation is a simple $2$-connected plane graph all of whose faces, the outer face included, are bounded by $k$-cycles; the face hypergraph of either is the $k$-uniform h...
Let $\alpha'(G)$ be the matching number of a graph $G$, and let its Randi\'c index be $R(G)=\sum_{uv\in E(G)}(d(u)d(v))^{-1/2}$. In 2006, Aouchiche, Hansen, and Zheng conjectured that the maximum of $R(G)-\alpha'(G)$ over all $n$-vertex graphs is attained by the complete bipartite graph whose smaller part has $\lfloor\...
Pei Liu, F. Nan, O. Suil et al.· 0 citations
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