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Feedback edge set in bipartite digraph
Bin Chen, Jianfeng Hou, Siyue Liu
Let \(β(G)\) denote the minimum size of a feedback edge set of a digraph \(G\), and let \(γ(G)\) denote the number of unordered pairs of nonadjacent vertices. Motivated by the Chud…
On the Erdős Five-Edge Intersection Problem
Chengrui Fang, Jianfeng Hou
For an -vertex graph and a permutation of its vertex set, let \[ I_G(π)=|E(G)\cap E(G_π)|,\qquad μ(G)=\min_π I_G(π), \] where is the copy of obtained by relabe…
On the Generalized Rational Exponents Conjecture
Jianfeng Hou, Caihong Yang
For fixed graphs and , let $\ex(n,H,F)$ denote the maximum number of copies of in an -vertex -free graph. In this note, we prove the generalized rational exponents…
Non-trivial Intersection Problems for Multi-partite Hypergraphs
Jianfeng Hou, Caiyun Hu
We study non-trivial intersection problems for multi-partite hypergraphs, excluding the usual extremal examples determined by fixed vertices or fixed coordinates. Our first result…
Local and global average degree in bipartite graphs
Jianfeng Hou, Hongbin Zhao
Let denote the maximum, over all -vertex bipartite graphs without isolated vertices, of the ratio of the minimum local average degree to the global average…
An Improved Upper Bound for Finite Sidon Sets via Vector-Valued Smoothing
Jianfeng Hou, Hongbin Zhao
Let denote the largest cardinality of a Sidon subset of . We prove \[ F(N)\le N^{1/2}+γ_0N^{1/4}+O(1), \qquad γ_0=0.94349\ldots<0.9435. \] This improves…