Zhen Liu

collaborators

11 papers

cond-mat.soft2026

Generalized Constraint-Controlled Rheological Model: Two Constitutive Pathways under Sinusoidal Periodic Shear Deformation

Dario Nichetti, Alessio Zaccone

We formulate the Generalized Constraint-Controlled Rheological Model (GCCRM) for entangled linear and long-arm-branched polymer melts under sinusoidal periodic shear deformation (S…

math.CO2026

Large induced subgraphs with $k$ vertices of maximum degree

Zhen liu, Qinghou Zeng

We prove that, for every integer $k \geq 2$ , there exists a constant $c_{k} > 0$ such that every graph on $n \geq R (k, k)$ vertices with maximum degree $Δ$ contains an induced subgraph on a…

math.CO2026

A sharp asymptotic bound for odd cycles in planar graphs

Zhen Liu, Chuanshu Wu

For graphs $G$ and $H$ , let $N (G, H)$ denote the number of unlabeled, not necessarily induced copies of $H$ in $G$ , and let $N_{P} (n, H)$ be the maximum of $…

math.CO2026

A subquadratic bound for generalized Turán numbers of odd cycles

Zhen Liu, Chuanshu Wu

For a graph $H$ and a family of graphs $F$ , let $ex (n, H, F)$ denote the maximum number of copies of $H$ in an $F$ -free graph on $n$ vertices. For e…

math.CO2026

Sharp asymptotics for triangle independence and covering numbers

Zhen Liu, Qinghou Zeng

For a graph $G$ , let $α_{1} (G)$ be the maximum size of an edge set containing at most one edge from every triangle, and let $τ_{1} (G)$ be the minimum size of an edge set meeting every…

math.CO2026

The maximum number of paths of even length in a planar graph

Zhen Liu, Chuanshu Wu

For graphs $G$ and $H$, let $N(G,H)$ be the number of unlabeled, not necessarily induced copies of $H$ in $G$, and let $f(n,H)$ be the maximum of $N(G,H)$ over all \(…

math.CO2026

Paths of even length with equal-degree endpoints

Kaizhe Chen, Zhen Liu, Qinghou Zeng

Addressing a question posed by Erdős and Hajnal, Chen and Ma proved that, for all $n \geq 600$ , the complete bipartite graph $K_{n, n + 1}$ is the unique graph on $2 n + 1$ vertices with…

math.CO2026

Degree sequences realizing labelled $h$ -factors

Zhen Liu, Qinghou Zeng

For a positive integer $ k $, let $ [k] = \{1, 2, \ldots, k\} $. Let $ h $ be a non-negative integer, and let $ n $ be a multiple of $ h + 1 $. Define $ H $ as the disj…

math.CO2026

Paths of length five with equal-degree endpoints

Zhen Liu, Qinghou Zeng

Addressing a question posed by Erdős and Hajnal, Chen and Ma proved that, for all $n \geq 600$ , the complete bipartite graph $K_{n, n + 1}$ is the unique graph on $2 n + 1$ vertices with…

math.CO2025

A complement of the Erdős-Hajnal problem on paths with equal-degree endpoints

Zhen Liu, Qinghou Zeng

Answering a question of Erdős and Hajnal, Chen and Ma proved that for all $n\geq600$ every graph with $2n + 1$ vertices and at least $n^2 + n+1$ edges contains two vertices o…

math.CO2025

Equating three degrees of graphs

Zhen Liu, Qinghou Zeng

In this paper, we prove that, for every graph with at least 5 vertices, one can delete at most 3 vertices such that the subgraph obtained has at least three vertices with the same…

Generalized Constraint-Controlled Rheological Model: Two Constitutive Pathways under Sinusoidal Periodic Shear Deformation

Large induced subgraphs with k vertices of maximum degree

A sharp asymptotic bound for odd cycles in planar graphs

A subquadratic bound for generalized Turán numbers of odd cycles

Sharp asymptotics for triangle independence and covering numbers

The maximum number of paths of even length in a planar graph

Paths of even length with equal-degree endpoints

Degree sequences realizing labelled h-factors

Paths of length five with equal-degree endpoints

A complement of the Erdős-Hajnal problem on paths with equal-degree endpoints

Equating three degrees of graphs

Large induced subgraphs with $k$ vertices of maximum degree

Degree sequences realizing labelled $h$ -factors