2 citations · 3 across the 9 of their papers we have counts for
10 papers
Polynomial Compressibility and Forbidden Oriented Forests
Zhenhua Lyu
For a nonempty acyclic oriented graph , let be the order of a longest directed path and let be the least positive integer such that admits a homomorphism t…
The Exact End-Degree Threshold for Finite-Width Directed Hexagonal Grids
Dan Zhu, Zhenhua Lyu
Grid theorems provide a fundamental link between the structure of ends and the existence of grid-like subgraphs in infinite graphs and digraphs. For every fixed width , let $k(n…
The Prescribed-Vertex Semidegree Threshold for Directed -Cycles in Oriented Graphs
Zhenhua Lyu
For every , we prove that every oriented graph on vertices whose minimum semidegree satisfies \[ δ^0(G)\ge \left\lceil\frac n3\right\rceil \] contains a dire…
A Sharp Ramsey Theorem for Admissible Colorings of Ordered Cliques
Yanan Hu, Zhenhua Lyu, Chenxi Yang
Let \(f(k)\) be the minimum integer \(N\) such that any red--blue edge-coloring of the ordered complete graph on \(N\) vertices contains a set of \(k\) vertices whose induced color…
Extremal digraphs containing at most paths of length 2 with the same endpoints
Zejun Huang, Zhenhua Lyu
Given a positive integer , let be the digraph consisting of directed paths of length 2 with the same initial and terminal vertices. In this paper, we study the max…
A note on extremal digraphs containing at most walks of length with the same endpoints
Zhenhua Lyu
Let be positive integers. What is the maximum number of arcs in a digraph on vertices in which there are at most distinct walks of length with the same endpoint…
Extremal digraphs avoiding distinct walks of length 3 with the same endpoints
Zejun Huang, Zhenhua Lyu
In this paper, we determine the maximum size of digraphs on vertices in which there are no two distinct walks of length with the same initial vertex and the same terminal v…
0-1 matrices with zero trace whose squares are 0-1 matrices
Zejun Huang, Zhenhua Lyu
In this paper, we determine the maximum number of nonzero entries in 0-1 matrices of order with zero trace whose squares are 0-1 matrices when . The extremal matrices a…
Extremal digraphs avoiding an orientation of
Zejun Huang, Zhenhua Lyu
Let be the orientation of which consists of two 2-paths with the same initial and terminal vertices. In this paper, we determine the maximum size of -free…
Turán problems for digraphs avoiding distinct walks of a given length with the same endpoints
Zejun Huang, Zhenhua Lyu, Pu Qiao
Let and be positive integers. We determine the maximum size of digraphs of order n that avoid distinct walks of length k with the same endpoints. We also charact…