arXiv subjects

Haixing Zhao

Publications and source records attributed to Haixing Zhao.

10 recordsLinked to original sources

arXiv2026

SketchGraphNet: A Memory-Efficient Hybrid Graph Transformer for Large-Scale Sketch Corpora Recognition

This work investigates large-scale sketch recognition from a graph-native perspective, where free-hand sketches are directly modeled as structured graphs rather than raster images or stroke sequences. We propose SketchGraphNet, a hybrid graph neural architecture that integrates local message passing with a memory-efficient global attention mechanism, without relying on auxiliary positional or structural encodings. To support systematic evaluation, we construct SketchGraph, a large-scale benchmark comprising 3.44 million graph-structured sketches across 344 categories, with two variants (A and R) to reflect different noise conditions. Each sketch is represented as a spatiotemporal graph with normalized stroke-order attributes. On SketchGraph-A and SketchGraph-R, SketchGraphNet achieves Top-1 accuracies of 83.62% and 87.61%, respectively, under a unified training configuration. MemEffAttn further reduces peak GPU memory by over 40% and training time by more than 30% compared with Performer-based global attention, while maintaining comparable accuracy.

cs.CV↗

arXiv2023

Momentum Gradient-based Untargeted Attack on Hypergraph Neural Networks

Hypergraph Neural Networks (HGNNs) have been successfully applied in various hypergraph-related tasks due to their excellent higher-order representation capabilities. Recent works have shown that deep learning models are vulnerable to adversarial attacks. Most studies on graph adversarial attacks have focused on Graph Neural Networks (GNNs), and the study of adversarial attacks on HGNNs remains largely unexplored. In this paper, we try to reduce this gap. We design a new HGNNs attack model for the untargeted attack, namely MGHGA, which focuses on modifying node features. We consider the process of HGNNs training and use a surrogate model to implement the attack before hypergraph modeling. Specifically, MGHGA consists of two parts: feature selection and feature modification. We use a momentum gradient mechanism to choose the attack node features in the feature selection module. In the feature modification module, we use two feature generation approaches (direct modification and sign gradient) to enable MGHGA to be employed on discrete and continuous datasets. We conduct extensive experiments on five benchmark datasets to validate the attack performance of MGHGA in the node and the visual object classification tasks. The results show that MGHGA improves performance by an average of 2% compared to the than the baselines.

cs.LG↗

arXiv2021

The Aging Effect in Evolving Scientific Citation Networks

The study of citation networks is of interest to the scientific community. However, the underlying mechanism driving individual citation behavior remains imperfectly understood, despite the recent proliferation of quantitative research methods. Traditional network models normally use graph theory to consider articles as nodes and citations as pairwise relationships between them. In this paper, we propose an alternative evolutionary model based on hypergraph theory in which one hyperedge can have an arbitrary number of nodes, combined with an aging effect to reflect the temporal dynamics of scientific citation behavior. Both theoretical approximate solution and simulation analysis of the model are developed and validated using two benchmark datasets from different disciplines, i.e. publications of the American Physical Society (APS) and the Digital Bibliography & Library Project (DBLP). Further analysis indicates that the attraction of early publications will decay exponentially. Moreover, the experimental results show that the aging effect indeed has a significant influence on the description of collective citation patterns. Shedding light on the complex dynamics driving these mechanisms facilitates the understanding of the laws governing scientific evolution and the quantitative evaluation of scientific outputs.

physics.soc-ph↗

arXiv2021

Uniformly most reliable three-terminal graph of dense graphs

A graph $G$ with $k$ specified target vertices in vertex set is a $k$-terminal graph. The $k$-terminal reliability is the connection probability of the fixed $k$ target vertices in a $k$-terminal graph when every edge of this graph survives independently with probability $p$. For the class of two-terminal graphs with a large number of edges, Betrand, Goff, Graves and Sun constructed a locally most reliable two-terminal graph for $p$ close to $1$, and illustrated by a counterexample that this locally most reliable graph is not the uniformly most reliable two-terminal graph. At the same time, they also determined that there is a uniformly most reliable two-terminal graph in the class obtained by deleting an edge from the complete graph with two target vertices. This article focuses on the uniformly most reliable three-terminal graph of dense graphs with $n$ vertices and $m$ edges. First, we give the locally most reliable three-terminal graphs of $n$ and $m$ in certain ranges for $p$ close to $0$ and $1$. Then, it is proved that there is no uniformly most reliable three-terminal graph with specific $n$ and $m$, where $n\geq7$ and $\binom{n}{2}-\lfloor\frac{n-3}{2}\rfloor\leq m\leq\binom{n}{2}-2$. Finally, some uniformly most reliable graphs are given for $n$ vertices and $m$ edges, where $4\leq n\leq 6$ and $m=\binom{n}{2}-2$ or $n\geq5$ and $m=\binom{n}{2}-1$.

math.CO↗

arXiv2017

Nordhaus-Gaddum-type theorem for conflict-free connection number of graphs

An edge-colored graph $G$ is \emph{conflict-free connected} if, between each pair of distinct vertices, there exists a path containing a color used on exactly one of its edges. The \emph{conflict-free connection number} of a connected graph $G$, denoted by $cfc(G)$, is defined as the smallest number of colors that are needed in order to make $G$ conflict-free connected. In this paper, we determine all trees $T$ of order $n$ for which $cfc(T)=n-t$, where $t\geq 1$ and $n\geq 2t+2 $. Then we prove that $1\leq cfc(G)\leq n-1$ for a connected graph $G$, and characterize the graphs $G$ with $cfc(G)=1,n-4,n-3,n-2,n-1$, respectively. Finally, we get the Nordhaus-Gaddum-type theorem for the conflict-free connection number of graphs, and prove that if $G$ and $\overline{G}$ are connected, then $4\leq cfc(G)+cfc(\overline{G})\leq n$ and $4\leq cfc(G)\cdot cfc(\overline{G})\leq2(n-2)$, and moreover, $cfc(G)+cfc(\overline{G})=n$ or $cfc(G)\cdot cfc(\overline{G})=2(n-2)$ if and only if one of $G$ and $\overline{G}$ is a tree with maximum degree $n-2$ or a $P_5$, and the lower bounds are sharp.

math.CO↗

arXiv2017

Conflict-free vertex-connections of graphs

A path in a vertex-colored graph is called \emph{conflict free} if there is a color used on exactly one of its vertices. A vertex-colored graph is said to be \emph{conflict-free vertex-connected} if any two vertices of the graph are connected by a conflict-free path. This paper investigates the question: For a connected graph $G$, what is the smallest number of colors needed in a vertex-coloring of $G$ in order to make $G$ conflict-free vertex-connected. As a result, we get that the answer is easy for $2$-connected graphs, and very difficult for connected graphs with more cut-vertices, including trees.

math.CO↗

arXiv2017

Conflict-free connection numbers of line graphs

A path in an edge-colored graph is called \emph{conflict-free} if it contains at least one color used on exactly one of its edges. An edge-colored graph $G$ is \emph{conflict-free connected} if for any two distinct vertices of $G$, there is a conflict-free path connecting them. For a connected graph $G$, the \emph{conflict-free connection number} of $G$, denoted by $cfc(G)$, is defined as the minimum number of colors that are required to make $G$ conflict-free connected. In this paper, we investigate the conflict-free connection numbers of connected claw-free graphs, especially line graphs. We first show that for an arbitrary connected graph $G$, there exists a positive integer $k$ such that $cfc(L^k(G))\leq 2$. Secondly, we get the exact value of the conflict-free connection number of a connected claw-free graph, especially a connected line graph. Thirdly, we prove that for an arbitrary connected graph $G$ and an arbitrary positive integer $k$, we always have $cfc(L^{k+1}(G))\leq cfc(L^k(G))$, with only the exception that $G$ is isomorphic to a star of order at least~$5$ and $k=1$. Finally, we obtain the exact values of $cfc(L^k(G))$, and use them as an efficient tool to get the smallest nonnegative integer $k_0$ such that $cfc(L^{k_0}(G))=2$.

math.CO↗

arXiv2016

On the Equitable Vertex Arboricity of Graphs

The equitable coloring problem, introduced by Meyer in 1973, has received considerable attention and research. Recently, Wu, Zhang and Li introduced the concept of equitable $(t,k)$-tree-coloring, which can be regarded as a generalization of proper equitable $t$-coloring. The \emph{strong equitable vertex $k$-arboricity} of $G$, denoted by ${va_k}^\equiv(G)$, is the smallest integer $t$ such that $G$ has an equitable $(t', k)$-tree-coloring for every $t'\geq t$. The exact value of strong equitable vertex $k$-arboricity of complete equipartition bipartite graph $K_{n,n}$ was studied by Wu, Zhang and Li. In this paper, we first get a sharp upper bound of strong equitable vertex arboricity of complete bipartite graph$K_{n,n+\ell} \ (1\leq \ell\leq n)$, that is, ${va_2}^\equiv(K_{n,n+\ell})\leq2\left\lfloor{\frac{n+\ell+1}{3}}\right\rfloor$. Next, we obtain a sufficient and necessary condition on an equitable $(q,\infty)$-tree coloring of a complete equipartition tripartite graph, and study the strong equitable vertex arboricity of forests. For a simple graph $G$ of order $n$, we show that $1\leq {va_k}^\equiv(G)\leq \lceil n/2 \rceil$. Furthermore, graphs with ${va_k}^\equiv(G)=1,\lceil\frac{n}{2}\rceil,\lceil\frac{n}{2}\rceil-1$ are characterized, respectively. In the end, we obtain the Nordhaus-Gaddum type results of strong equitable vertex $k$-arboricity for general $k$.

math.CO↗

arXiv2015

On the regular k-independence number of graphs

The \emph{regular independence number}, introduced by Albertson and Boutin in 1990, is the maximum cardinality of an independent set of $G$ in which all vertices have equal degree in $G$. Recently, Caro, Hansberg and Pepper introduced the concept of regular $k$-independence number, which is a natural generalization of the regular independence number. A \emph{$k$-independent set} is a set of vertices whose induced subgraph has maximum degree at most $k$. The \emph{regular $k$-independence number} of $G$, denoted by $α_{k-reg}(G)$, is defined as the maximum cardinality of a $k$-independent set of $G$ in which all vertices have equal degree in $G$. In this paper, the exact values of the regular $k$-independence numbers of some special graphs are obtained. We also get some lower and upper bounds for the regular $k$-independence number of trees with given diameter, and the lower bounds for the regular $k$-independence number of line graphs. For a simple graph $G$ of order $n$, we show that $1\leqα_{k-reg}(G)\leq n$ and characterize the extremal graphs. The Nordhaus-Gaddum-type results for the regular $k$-independence number of graphs are also obtained.

math.CO↗

arXiv2015

On the equitable vertex arboricity of complete tripartite graphs

The equitable coloring problem, introduced by Meyer in 1973, has received considerable attention and research. Recently, Wu et al. introduced the concept of equitable (t,k)-tree-coloring, which can be viewed as a generalization of proper equitable t-coloring. The strong equitable vertex k-arboricity of complete bipartite equipartition graphs was investigated in 2013. In this paper, we study the exact value of the strong equitable vertex 3-arboricity of complete equipartition tripartite graphs.

math.CO↗