arXiv subjects

Mengyuan Niu

Publications and source records attributed to Mengyuan Niu.

7 recordsLinked to original sources

arXiv2026

Sim-Width, Induced Matching Treewidth, and Tree-Independence Number in Induced $K_{t,t}$-Free Graphs

The tree-independence number $tree\text{-}α(G)$, the induced matching treewidth $tree\text{-}μ(G)$, and the sim-width $simw(G)$ are graph parameters defined in terms of tree or branch decompositions. We establish two polynomial bounds for the tree-independence number of induced $K_{t,t}$-free graphs, one in terms of sim-width and the other in terms of induced matching treewidth. Abrishami et al. (SIDMA, 2025) and Brettell et al. (EJC, 2025) asked whether bounded sim-width, together with the exclusion of an induced $K_{t,t}$, implies bounded tree-independence number. We answer this question by proving that, for integers $t\geq 2$ and $s\geq 1$, every induced $K_{t,t}$-free graph $G$ with $simw(G)\leq s$ satisfies $tree\text{-}α(G)=O_t\left((s+1)^{2t^2-2t}\right)$. This also proves a polynomial strengthening of a conjecture of Bešter Štorgel et al. (arXiv, 2026) concerning induced $K_{1,t}$-free graphs and improves a theorem of Alon et al. (arXiv, 2025) by reducing the exponent from $3t^2+1$ to $2t^2-2t$. Alon et al. (arXiv, 2025) asked whether, for fixed induced matching treewidth, the tree-independence number is polynomially bounded in $t$. Using a VC-dimension argument, we answer this question affirmatively by showing that, for integers $μ\geq 1$ and $t\geq 2$, every induced $K_{t,t}$-free graph $G$ with $tree\text{-}μ(G)\leqμ$ satisfies $tree\text{-}α(G)=t^{O_μ(1)}$.

math.CO↗

arXiv2026

Tight Staircase Bounds for Cyclic Subsets below Dirac's Threshold

Let $\operatorname{Cyc}(G)$ denote the number of cyclic subsets in a graph $G$, which are subsets that induce a Hamiltonian subgraph. Draganić, Keevash and Müyesser recently proved that every regular Dirac graph has $Ω(2^n)$ cyclic subsets, resolving a problem of Erdős and Faudree. We determine the sharp asymptotic lower bound throughout the linear range below Dirac's threshold. Let $G$ be an $n$-vertex $d$-regular graph with $d=Ω(n)$ and $d<n/2$, then $$ \operatorname{Cyc}(G)\ge (q-o(1))2^{n/q}, \quad \text{where } \quad q=\left\lfloor \frac{n}{d+1}\right\rfloor \ge 2. $$ This bound is asymptotically best possible, including the leading coefficient $q$, as witnessed at the staircase levels by the disjoint union of $q$ equal cliques. Consequently, the optimal exponential rate changes by discrete jumps as $d$ crosses the thresholds $n/k$, rather than varying smoothly with $d$. We also prove the optimal exponential rate at the Dirac boundary: every $n$-vertex $n/2$-regular graph satisfies $\operatorname{Cyc}(G)\ge 2^{(1-o(1))n},$ which is sharp up to a subexponential factor by $K_{n/2,n/2}$.

math.CO↗

arXiv2026

An exact robust Ramsey theorem for matchings

Keevash and Michaeli recently proved that, under the robustness assumption that $G$ is an $s$-connector (i.e. $\overline G$ is $K_{s,s}$-free), $G$ has essentially the same multicolour Ramsey matching properties as complete graphs, with an additive error $O(qs)$, where $q$ is the number of colours. They asked whether the dependence on $q$ can be removed. We answer this question in a stronger exact form. For ${\bf t}=(t_1,\ldots,t_q)\in\mathbb N_+^q$, let $R_s({\bf t})$ be the smallest integer $N$ such that every $N$-vertex $s$-connector $G$ satisfies $ G\to (t_1K_2,\ldots,t_qK_2). $ We determine the exact value \[ R_s({\bf t})=\sum_{j\in[q]}(t_j-1)+ \max\left\{2s,\ s+\max_{j\in[q]}t_j\right\}. \] While Keevash and Michaeli's proof uses a compression algorithm based on the Gallai--Edmonds decomposition to reduce the colouring to a structured form, our proof is a direct minimal-counterexample argument together with a new counting method for monochromatic matchings which can be applied to $s$-connectors.

math.CO↗

arXiv2026

Diagnosing Urban Street Vitality via a Visual-Semantic and Spatiotemporal Framework for Street-Level Economics

Micro-scale street-level economic assessment is fundamental for precision spatial resource allocation. While Street View Imagery (SVI) advances urban sensing, existing approaches remain semantically superficial and overlook brand hierarchy heterogeneity and structural recession. To address this, we propose a visual-semantic and field-based spatiotemporal framework, operationalized via the Street Economic Vitality Index (SEVI). Our approach integrates physical and semantic streetscape parsing through instance segmentation of signboards, glass interfaces, and storefront closures. A dual-stage VLM-LLM pipeline standardizes signage into global hierarchies to quantify a spatially smoothed brand premium index. To overcome static SVI limitations, we introduce a temporal lag design using Location-Based Services (LBS) data to capture realized demand. Combined with a category-weighted Gaussian spillover model, we construct a three-dimensional diagnostic system covering Commercial Activity, Spatial Utilization, and Physical Environment. Experiments based on time-lagged geographically weighted regression across eight tidal periods in Nanjing reveal quasi-causal spatiotemporal heterogeneity. Street vibrancy arises from interactions between hierarchical brand clustering and mall-induced externalities. High-quality interfaces show peak attraction during midday and evening, while structural recession produces a lagged nighttime repulsion effect. The framework offers evidence-based support for precision spatial governance.

cs.CY↗

arXiv2025

The spectral radii and extremal graphs of two types of minimal graphs

A connected nontrivial graph $G$ is {\it matching covered} if every edge of $G$ is contained in some perfect matching of $G$. A matching covered graph $G$ is {\it minimal} if $G-e$ is not matching covered for each edge $e$ of $G$. A graph is said to be {\it factor-critical} if $G-v$ has a perfect matching for every $v\in V(G)$. A factor-critical graph $G$ is said to be {\it minimal factor-critical} if $G-e$ is not factor-critical graph for each edge $e\in E(G)$. In this paper, by employing ear decomposition and edge-exchange techniques, the greatest spectral radii of minimal matching covered bipartite graphs and minimal factor-critical graphs are determined, and the corresponding extremal graphs are characterized.

math.CO↗

arXiv2025

Controllable Generation of Large-Scale 3D Urban Layouts with Semantic and Structural Guidance

Urban modeling is essential for city planning, scene synthesis, and gaming. Existing image-based methods generate diverse layouts but often lack geometric continuity and scalability, while graph-based methods capture structural relations yet overlook parcel semantics. We present a controllable framework for large-scale 3D vector urban layout generation, conditioned on both geometry and semantics. By fusing geometric and semantic attributes, introducing edge weights, and embedding building height in the graph, our method extends 2D layouts to realistic 3D structures. It also enables users to directly control the output by modifying semantic attributes. Experiments show that it produces valid, large-scale urban models, offering an effective tool for data-driven planning and design.

cs.CV↗

arXiv2024

Enhancement of 3D Gaussian Splatting using Raw Mesh for Photorealistic Recreation of Architectures

The photorealistic reconstruction and rendering of architectural scenes have extensive applications in industries such as film, games, and transportation. It also plays an important role in urban planning, architectural design, and the city's promotion, especially in protecting historical and cultural relics. The 3D Gaussian Splatting, due to better performance over NeRF, has become a mainstream technology in 3D reconstruction. Its only input is a set of images but it relies heavily on geometric parameters computed by the SfM process. At the same time, there is an existing abundance of raw 3D models, that could inform the structural perception of certain buildings but cannot be applied. In this paper, we propose a straightforward method to harness these raw 3D models to guide 3D Gaussians in capturing the basic shape of the building and improve the visual quality of textures and details when photos are captured non-systematically. This exploration opens up new possibilities for improving the effectiveness of 3D reconstruction techniques in the field of architectural design.

cs.CV↗