2024/11/27 by Yu Chen, Jie Han, Chen, Yu +3 · 1 citation
Computer Science · #Rough Sets and Fuzzy Logic
paper · pdf · doi:10.48550/arxiv.2411.18596
An n-vertex k-uniform hypergraph G is (d,α)-degenerate if m1(G)≤d and there exists a constant ε >0 such that for every subset U⊆V(G) with size 2≤|U|≤ε n, we have e(G[U])≤d(|U|-1)-α. These hypergraphs include many natural graph classes, such as the degenerate hypergraphs, the planar graphs, and the power of cycles. In this paper, we consider the threshold of the emergence of a (d,α)-degenerate hypergraph with bounded maximum degree in the Erdős-Rényi model. We show that its threshold is at most n-1/d, improving previous results of Riordan and Kelly-Müyesser-Pokrovskiy.