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Qiannan Zhou

Publications and source records attributed to Qiannan Zhou.

9 recordsLinked to original sources

RefAdapt-DiT: Adaptive Joint Attention for Reference-Conditioned Diffusion Transformers

Diffusion Transformers (DiTs) have become the standard backbone for high-quality generative modeling, yet deploying them in conditional generation tasks remains computationally prohibitive because bidirectional joint attention repeatedly processes large reference streams. While existing optimization schemes mitigate generic temporal redundancy, they typically rely on coarse-grained static reuse and overlook the distinct dynamics of references and targets. Specifically, we observe that reference representations often evolve slowly along the generation trajectory, while the target often assigns little attention mass to them; reference drift and this target-to-reference exposure jointly shape how strongly stale reference states affect the target. To exploit these patterns, we introduce \RefAdapt, a training-free framework for adaptive control of joint attention between references and targets. Instead of rigid static strategies, \RefAdapt combines consecutive target-Q change with previously observed target-to-reference attention mass to control reference computation adaptively at block granularity. Under ultra-few-step settings, \RefAdapt enables speedups of up to $2.097\times$ on 4-step MiniMax H3 and $3.54\times$ on 8-step Qwen Image Edit, while maintaining comparable visual quality.

cs.CV↗

Hamiltonian cycles in 7-tough $(P_4\cup P_1)$-free graphs

Shan~[J. Graph Theory (2026)] proved that every 23-tough $(P_4\cup P_1)$-free graph on at least three vertices is Hamiltonian. We improve this bound to 7 by replacing the final cut analysis in Shan's framework with an asymmetric separation criterion and a cograph covering lemma.

math.CO↗

Distance signless Laplacian spectral radius and tough graphs involving minimun degree

Let $G=(V(G),E(G))$ be a simple graph, where $V(G)$ and $E(G)$ are the vertex set and the edge set of $G$, respectively. The number of components of $G$ is denoted by $c(G)$. Let $t$ be a positive real number, and a connected graph $G$ is $t$-tough if $t c(G-S)\leq|S|$ for every vertex cut $S$ of $V(G)$. The toughness of graph $G$, denoted by $τ(G)$, is the largest value of $t$ for which $G$ is $t$-tough. Recently, Fan, Lin and Lu [European J. Combin. 110(2023), 103701] presented sufficient conditions based on the spectral radius for graphs to be 1-tough with minimum degree $δ(G)$ and graphs to be $t$-tough with $t\geq 1$ being an integer, respectively. In this paper, we establish sufficient conditions in terms of the distance signless Laplacian spectral radius for graphs to be 1-tough with minimum degree $δ(G)$ and graphs to be $t$-tough, where $\frac{1}{t}$ is a positive integer. Moreover, we consider the relationship between the distance signless Laplacian spectral radius and $t$-tough graphs in terms of the order $n$.

math.CO↗

The rank of a complex unit gain graph in terms of the rank of its underlying graph

Let $Φ=(G, φ)$ be a complex unit gain graph (or $\mathbb{T}$-gain graph) and $A(Φ)$ be its adjacency matrix, where $G$ is called the underlying graph of $Φ$. The rank of $Φ$, denoted by $r(Φ)$, is the rank of $A(Φ)$. Denote by $θ(G)=|E(G)|-|V(G)|+ω(G)$ the dimension of cycle spaces of $G$, where $|E(G)|$, $|V(G)|$ and $ω(G)$ are the number of edges, the number of vertices and the number of connected components of $G$, respectively. In this paper, we investigate bounds for $r(Φ)$ in terms of $r(G)$, that is, $r(G)-2θ(G)\leq r(Φ)\leq r(G)+2θ(G)$, where $r(G)$ is the rank of $G$. As an application, we also prove that $1-θ(G)\leq\frac{r(Φ)}{r(G)}\leq1+θ(G)$. All corresponding extremal graphs are characterized.

math.CO↗

Skew-rank of an oriented graph in terms of the rank and dimension of cycle space of its underlying graph

Let $G^σ$ be an oriented graph and $S(G^σ)$ be its skew-adjacency matrix, where $G$ is called the underlying graph of $G^σ$. The skew-rank of $G^σ$, denoted by $sr(G^σ)$, is the rank of $S(G^σ)$. Denote by $d(G)=|E(G)|-|V(G)|+θ(G)$ the dimension of cycle spaces of $G$, where $|E(G)|$, $|V(G)|$ and $θ(G)$ are the edge number, vertex number and the number of connected components of $G$, respectively. Recently, Wong, Ma and Tian [European J. Combin. 54 (2016) 76--86] proved that $sr(G^σ)\leq r(G)+2d(G)$ for an oriented graph $G^σ$, where $r(G)$ is the rank of the adjacency matrix of $G$, and characterized the graphs whose skew-rank attain the upper bound. However, the problem of the lower bound of $sr(G^σ)$ of an oriented graph $G^σ$ in terms of $r(G)$ and $d(G)$ of its underlying graph $G$ is left open till now. In this paper, we prove that $sr(G^σ)\geq r(G)-2d(G)$ for an oriented graph $G^σ$ and characterize the graphs whose skew-rank attain the lower bound.

math.CO↗

Hermitian-Randić matrix and Hermitian-Randić energy of mixed graphs

Let $M$ be a mixed graph and $H(M)$ be its Hermitian-adjacency matrix. If we add every edge and arc in $M$ a Randić weight, then we can get a new weighted Hermitian-adjacency matrix. What are the properties of this new matrix? Motivated by this, we define the Hermitian-Randić matrix $R_{H}(M)=(r_{h})_{kl}$ of a mixed graph $M$, where $(r_{h})_{kl}=-(r_{h})_{lk}=\frac{\textbf{i}}{\sqrt{d_{k}d_{l}}}$ ($\textbf{i}=\sqrt{-1}$) if $(v_{k},v_{l})$ is an arc of $M$, $(r_{h})_{kl}=(r_{h})_{lk}=\frac{1}{\sqrt{d_{k}d_{l}}}$ if $v_{k}v_{l}$ is an undirected edge of $M$, and $(r_{h})_{kl}=0$ otherwise. In this paper, firstly, we compute the characteristic polynomial of the Hermitian-Randić matrix of a mixed graph. Furthermore, we give bounds to the Hermitian-Randić energy of a general mixed graph. Finally, we give some results about the Hermitian-Randić energy of mixed trees.

math.CO↗

Distance signless Laplacian spectral radius and Hamiltonian properties of graphs

In this paper, first, we establish a sufficient condition for a bipartite graph to be Hamilton-connected. Furthermore, we also give two sufficient conditions on distance signless Laplacian spectral radius for a graph to be Hamilton-connected and traceable from every vertex, respectively. Last, we obtain a sufficient condition for a graph to be Hamiltonian in terms of the distance signless Laplacian spectral radius of $G^{C}$.

math.CO↗