Lei Zhang

THE SPANNING K -HYPERTREE AND ADJACENCY SPECTRAL RADIUS IN HYPERGRAPHS ∗

The spanning $k$-hypertree and adjacency spectral radius in hypergraphs

The spanning $k$-tree of a connected graph is a spanning tree with a maximum degree not exceeding $k$. Hypergraphs provide a natural framework for modeling higher-order interactions. It is natural to extend the concept of spanning $k$-trees from graphs to hypergraphs. Tensor-based spectral models for hypergraphs are in...

Linear Turán Bounds for Hypertrees and Tight Bounds for 2P2 in Linear 3-Graph

Let H be an m-uniform hypergraph (m-graph), where m≥2. If any two hyperedges in H share at most one vertex, then H is an m-uniform linear hypergraph. Let F be a given family of m-graphs. H is called F-free if H does not contain any hypergraph in F as it is subhypergraph. The linear Turán number exmlin(n,F) of F is defi...