arXiv subjects

Yaobin Chen

Publications and source records attributed to Yaobin Chen.

At least 19 recordsLinked to original sources

arXiv2026

Small circumference in regular sublinear expanders

Sublinear expansion is weak enough to be extracted from arbitrary graphs while retaining nearly all of their average degree, yet it has proved strong enough to force global structures in many sparse extremal problems. Letzter, Methuku and Sudakov [JLMS 2026] proved the existence of nearly Hamilton cycles in sufficiently dense regular sublinear expanders. Montgomery [ICM 2026] subsequently conjectured that, every $d$-regular sublinear expander with $d$ sufficiently large (but constant) is Hamiltonian. We disprove this conjecture in a strong form by constructing $n$-vertex $d$-regular sublinear expanders with $d=\left(\frac12+o(1)\right)\log^2 n$, which can forbid any cycle covering an arbitrarily small given positive constant portion of its vertices. The construction blows up one side of a biregular Ramanujan graph into almost-complete blocks and keeps the other side as a sparse vertex separator. We also prove a similar statement for a closely related notion of edge expanders. For every sufficiently small $γ>0$, there is an infinite family of $n$-vertex $d$-regular $γ$-edge-expanders with $d=Θ(γ^{-1})$ and circumference $O(γn)$, matching the standard lower bound $Ω(γn)$. The construction also comes from an expanding regular core such that each vertex has an almost-complete graph attached to it. The core guarantees edge expansion, while the single-vertex attachments confine every cycle.

math.CO↗

arXiv2026

The Erdős-Gallai bound for consecutive even cycle lengths

Erdős and Gallai in 1959 proved the seminal result that every $n$-vertex graph with no cycle of length at least $2t+2$ has at most $\tfrac{2t+1}{2}(n-1)$ edges. We prove the extension that, for every sufficiently large $t$, the same quantity is also the sharp extremal bound for graphs with no $t$ consecutive even cycle lengths, resolving a conjecture of Verstraëte. Thus, at the Erdős-Gallai threshold, forcing an entire interval of even cycle lengths costs no more than forcing its longest member. More precisely, every $n$-vertex graph $G$ with $e(G)\ge \tfrac{(2t+1)(n-1)}2$ $\bullet$ either contains $t$ consecutive even cycle lengths, $\bullet$ or equality holds and $G$ is connected with every block isomorphic to $K_{2t+1}$. As consequences, for every sufficiently large even $k$ we determine the sharp edge thresholds forcing a cycle of length $0\pmod k$ or $2\pmod k$, answering questions of Bai, Grzesik, Li, and Prorok and of Gao, Li, Ma and Xie, respectively, for sufficiently large even $k$. The proof develops a stability-enhanced sublinear expander method. Its main new ingredient is a dense-case decomposition that recovers the lengths lost in the expander extraction by combining a flexible dense core with rooted cycle families in the vertices outside the core.

math.CO↗

arXiv2026

Tight Hamiltonian Cycles in Uniformly Dense $3$-Graphs

We study minimum degree conditions for tight Hamiltonian cycles in uniformly dense $3$-uniform hypergraphs. We prove that for every $d,α>0$, every sufficiently large $(ρ,d)$-dense $3$-graph on $n$ vertices with minimum codegree at least $(1/3+α)n$ contains a tight Hamiltonian cycle. This resolves a problem of Aigner-Horev and Levy in a stronger form, and the constant $1/3$ is asymptotically best possible. We also show that uniform density does not lower the asymptotic vertex-degree threshold: there are $(ρ,d)$-dense $3$-graphs with minimum vertex degree $(5/9-o(1))\binom{n}{2}$ and no tight Hamiltonian cycle. Finally, we construct $(ρ,2-\sqrt{3})$-dense examples with minimum codegree $(2-\sqrt{3}-o(1))n$ and no tight Hamiltonian cycle, answering negatively a question of Ara{ú}jo, Piga and Schacht.

math.CO↗

arXiv2026

OmniV2X: A Generative Foundation Planner for Efficient End-to-End Cooperative Driving

We present OmniV2X, a generative foundation model for vehicle-to-everything (V2X) cooperative driving. The model directly interprets independent context sequences comprising multi-modal and multi-agent observations. The new design mitigates the computational cost of dense 3D perception, the vulnerability to data scarcity in cooperative scenarios, and the poor compliance with standardized messaging in existing methods that fuse multi-modal inputs into a shared representation. For training, we present an end-to-end supervised pipeline using a downstream trajectory generation loss, in which a high-capacity generative sequence planner implicitly learns to steer the model and leverage multi-modal inputs via cross-attention injection. As a foundation model, we demonstrate that OmniV2X pre-trained on large-scale single-agent planning datasets can efficiently adapt to cooperative environments by integrating the conditioning context with lightweight, standard-compliant V2X tokens. Evaluated on the DAIR-V2X-Seq dataset, OmniV2X outperforms existing end-to-end cooperative driving baselines, achieving state-of-the-art performance with less than 10% of the fine-tune V2X dataset and less than 1% of the communication bandwidth. We conduct comprehensive evaluations to demonstrate its computational efficiency and robustness under real-world constraints.

cs.RO↗

arXiv2026

FleetAgent: Teleoperation Assistant for Autonomous Fleets via Vectorized V2N Messages

Large-scale autonomous fleets rely on teleoperation to resolve rare failures, yet streaming raw sensor data from many vehicles is costly, and remote operators can only monitor a limited number of vehicles at a time. We introduce FleetAgent, a cloud-hosted multimodal large language model (MLLM) assistant that consumes compact vectorized vehicle-to-network (V2N) messages, such as map elements, detected objects, and the ego planned path. It provides a structured natural-language response (including narration, explanation, and evaluation of the plan and scene), along with an intervention urgency score for operator prioritization. To make structured messages compatible with token-based MLLMs, we propose VecFormer, a vector-to-embedding interface with differentiable top-K context selection that bounds context length and GPU KV-cache growth, enabling more efficient batch processing, which is important under the context of cloud-hosted large-scale fleet management. We also construct VecEval, a nuScenes-derived dataset with paired human and synthetic imperfect plans and human-verified language labels, to facilitate the training and evaluation of our proposed system. Our proposed system can reduce uplink payload by up to 625 times compared with raw images and reduce KV-cache memory by 16.54 times compared with original text descriptions. On VecEval, FleetAgent improves Lingo-Judge score by 16.8% and reduces intervention failure rate by 19.9%, compared with Qwen2.5-VL-7B using language descriptions. These results demonstrate that FleetAgent can utilize compact structured V2N messaging to enable efficient, explainable teleoperation monitoring for autonomous fleets.

cs.RO↗

arXiv2026

Upper Bounds on Turán Densities via Extremal Set Theory

We exhibit, in a systematic way, connections between hypergraph Turán problems and extremal set theory. More specifically, we construct natural families of uniform hypergraphs for which the upper bounds on their Turán densities reduce to classical problems in extremal set theory, including the Erdős--Ko--Rado theorem, $L$-intersecting families, and the Erdős matching problem.

math.CO↗

arXiv2026

PSI: A Benchmark for Human Interpretation and Response in Traffic Interactions

Accurately modeling pedestrian intention and understanding driver decision-making processes are critical for the development of safe and socially aware autonomous driving systems. We introduce PSI, a benchmark dataset that captures the dynamic evolution of pedestrian crossing intentions from the driver's perspective, enriched with human textual explanations that reflect the reasoning behind intention estimation and driving decision making. These annotations offer a unique foundation for developing and benchmarking models that combine predictive performance with interpretable and human-aligned reasoning. PSI supports standardized tasks and evaluation protocols across multiple dimensions, including pedestrian intention prediction, driver decision modeling, reasoning generation, and trajectory forecasting and more. By enabling causal and interpretable evaluation, PSI advances research toward autonomous systems that can reason, act, and explain in alignment with human cognitive processes.

cs.CV↗

arXiv2026

Dynamic Risk Generation for Autonomous Driving: Naturalistic Reconstruction of Vehicle-E-Scooter Interactions

The increasing, high-risk interactions between vehicles and vulnerable micromobility users, such as e-scooter riders, challenge vehicular safety functions and Automated Driving (AD) techniques, often resulting in severe consequences due to the dynamic uncertainty of e-scooter motion. Despite advances in data-driven AD methods, traffic data addressing the e-scooter interaction problem, particularly for safety-critical moments, remains underdeveloped. This paper proposes a pipeline that utilizes collected on-road traffic data and creates configurable synthetic interactions for validating vehicle motion planning algorithms. A Social Force Model (SFM) is applied to offer more dynamic and potentially risky movements for the e-scooter, thereby testing the functionality and reliability of the vehicle collision avoidance systems. A case study based on a real-world interaction scenario was conducted to verify the practicality and effectiveness of the established simulator. Simulation experiments successfully demonstrate the capability of extending the target scenario to more critical interactions that may result in a potential collision.

eess.SY↗

arXiv2026

LLM4AD: Large Language Models for Autonomous Driving -- Concept, Review, Benchmark, Experiments, and Future Trends

With the broader adoption and highly successful development of Large Language Models (LLMs), there has been growing interest and demand for applying LLMs to autonomous driving technology. Driven by their natural language understanding and reasoning capabilities, LLMs have the potential to enhance various aspects of autonomous driving systems, from perception and scene understanding to interactive decision-making. This paper first introduces the novel concept of designing Large Language Models for Autonomous Driving (LLM4AD), followed by a review of existing LLM4AD studies. Then, a comprehensive benchmark is proposed for evaluating the instruction-following and reasoning abilities of LLM4AD systems, which includes LaMPilot-Bench, CARLA Leaderboard 1.0 Benchmark in simulation and NuPlanQA for multi-view visual question answering. Furthermore, extensive real-world experiments are conducted on autonomous vehicle platforms, examining both on-cloud and on-edge LLM deployment for personalized decision-making and motion control. Next, the future trends of integrating language diffusion models into autonomous driving are explored, exemplified by the proposed ViLaD (Vision-Language Diffusion) framework. Finally, the main challenges of LLM4AD are discussed, including latency, deployment, security and privacy, safety, trust and transparency, and personalization.

cs.RO↗

arXiv2026

Hitting time for Hamilton cycles in pseudorandom graphs

Consider the random subgraph process on a base graph $G$ with $n$ vertices: we generate a sequence $\{G_t\}_{t=0}^{|E(G)|}$ by taking a uniformly random ordering of the edges of $G$ and then adding these edges one by one to the empty graph $G_0$ on the same vertex set. We prove that there is a constant $C > 0$ such that if $G$ is an $(n,d,λ)$-graph with $d/λ\ge C$, then with high probability, the hitting time for the appearance of a Hamilton cycle coincides with the hitting time for reaching minimum degree $2$. This resolves questions posed by Alon--Krivelevich in 2019 and by Frieze--Krivelevich in 2002. As a consequence, we determine the sharp threshold for Hamilton cycles in $(n,d,λ)$-graphs with $d/λ\ge C$ for all $d$ sufficiently large. Lastly, we extend our result to the minimum degree $2k$ versus $k$ edge-disjoint Hamilton cycles setting for $k \leq c\cdot \min\{d,\log n\}$ where $c$ is a constant depending on $C$. This advances on a question asked by Frieze.

math.CO↗

arXiv2026

Note on the trace of random walks on pseudorandom graphs

We study the graph-theoretic properties of the trace of random walks on pseudorandom graphs. We show that for any $\varepsilon>0$, there exists a constant $C$ such that the cover time of an $(n,d,λ)$-graph $G$ with $d/λ\ge C$ is at most $(1+\varepsilon)n\log n$, meaning the expected number of steps needed to reach all vertices at least once is at most $(1+\varepsilon)n\log n$ regardless of the starting vertex. Furthermore, we prove that with high probability, the trace of a random walk of length $(1+\varepsilon)n\log n$ on $G$ is Hamiltonian, regardless of the starting vertex. These results also hold for random $d$-regular graphs with sufficiently large $d$. These findings answer two questions proposed by Frieze, Krivelevich, Michaeli, and Peled [PLMS, 2018]. Notably, our results imply a bound on a stronger version of the cover time: with high probability, all vertices are covered after $(1+\varepsilon)n\log n$ steps, regardless of the starting vertex. Our proofs rely on the spectral properties of the adjacency matrix and the graph expansion. All results are asymptotically optimal.

math.CO↗

arXiv2025

Robustness for expander graphs

We study robust versions of properties of $(n,d,λ)$-graphs, namely, the property of a random sparsification of an $(n,d,λ)$-graph, where each edge is retained with probability $p$ independently. We prove such results for the containment problem of perfect matchings, Hamiltonian cycles, and triangle factors. These results address a series of problems posed by Frieze and Krivelevich. First we prove that given $γ>0$, for sufficient large $n$, any $(n,d,λ)$-graph $G$ with $λ=o(d)$, $d=Ω(\log n)$ and $p\ge\frac{(1+γ)\log n}{d}$, $G\cap G(n,p)$ contains a Hamiltonian cycle (and thus a perfect matching if $n$ is even) with high probability. This result is asymptotically optimal. Moreover, we show that for sufficient large $n$, any $(n,d,λ)$-graph $G$ with $λ=o(\frac{d^2}{n})$, $d=Ω(n^{\frac{5}{6}}\log^{\frac{1}{2}}n)$ and $p\gg d^{-1}n^{\frac{1}{3}}\log^{\frac{1}{3}} n$, $G\cap G(n,p)$ contains a triangle factor with high probability. Here, the restrictions on $p$ and $λ$ are asymptotically optimal. Our proof for the triangle factor problem uses the iterative absorption approach to build a spread measure on the triangle factors, and we also prove and use a coupling result for triangles in the random subgraph of an expander $G$ and the hyperedges in the random subgraph of the triangle-hypergraph of $G$.

math.CO↗

arXiv2025

A Configurable Simulation Framework for Safety Assessment of Vulnerable Road Users

Ensuring the safety of vulnerable road users (VRUs), including pedestrians, cyclists, electric scooter riders, and motorcyclists, remains a major challenge for advanced driver assistance systems (ADAS) and connected and automated vehicles (CAV) technologies. Real-world VRU tests are expensive and sometimes cannot capture or repeat rare and hazardous events. In this paper, we present a lightweight, configurable simulation framework that follows European New Car Assessment Program (Euro NCAP) VRU testing protocols. A rule-based finite-state machine (FSM) is developed as a motion planner to provide vehicle automation during the VRU interaction. We also integrate ego-vehicle perception and idealized Vehicle-to-Everything (V2X) awareness to demonstrate safety margins in different scenarios. This work provides an extensible platform for rapid and repeatable VRU safety validation, paving the way for broader case-study deployment in diverse, user-defined settings, which will be essential for building a more VRU-friendly and sustainable intelligent transportation system.

eess.SY↗

arXiv2025

Limit for Quotient Convergent Graph Sequence

Building on the limit theory for set functions, we prove that the limit of convergent sequence of bounded-degree graphs' cycle matroids can be represented as the cycle matroid of a graphing, analogous to the completeness result for local-global convergence.

math.CO↗

arXiv2025

Maximum in-general-position set in a random subset of $\mathbb{F}^d_q$

Let $α(\mathbb{F}_q^{d},p)$ be the maximum possible size of a point set in general position in a $p$-random subset of $\mathbb{F}_q^d$. We determine the order of magnitude of $α(\mathbb{F}_q^{d},p)$ up to a polylogarithmic factor by proving the balanced supersaturation conjecture of Balogh and Luo. Our result also resolves a conjecture implicitly posed by the first author, Liu, the second author and Zeng. In the course of our proof, we establish a lemma that demonstrates a ``structure vs. randomness'' phenomenon for point sets in finite-field linear spaces, which may be of independent interest.

math.CO↗

arXiv2025

Unbounded degree spanning hypertrees in Dirac hypergraphs

In 2001, Komlós, Sárközy, and Szemerédi proved that every sufficiently large $n$-vertex graph with minimum degree at least $\left(1/2+γ\right)n$ contains all spanning trees with maximum degree at most $cn/\log n$. We extend this result to hypergraphs by considering loose hypertrees, which are linear hypergraphs obtained by successively adding edges that share exactly one vertex with a previous edge. For all $k > \ell \geq 2$, we determine asymptotically optimal $\ell$-degree conditions that ensure the existence of all rooted spanning loose hypertrees, without any degree condition, in terms of the $(\ell-1)$-degree threshold for the existence of a perfect matching in $(k-1)$-graphs. As a corollary, we also asymptotically determine the $\ell$-degree threshold for the existence of bounded degree spanning loose hypertrees in $k$-graphs for $k/2 < \ell < k$, confirming a conjecture of Pehova and Petrova in this range. In our proof, we avoid the use of Szemerédi's regularity lemma.

math.CO↗

arXiv2025

Lane-Wise Highway Anomaly Detection

This paper proposes a scalable and interpretable framework for lane-wise highway traffic anomaly detection, leveraging multi-modal time series data extracted from surveillance cameras. Unlike traditional sensor-dependent methods, our approach uses AI-powered vision models to extract lane-specific features, including vehicle count, occupancy, and truck percentage, without relying on costly hardware or complex road modeling. We introduce a novel dataset containing 73,139 lane-wise samples, annotated with four classes of expert-validated anomalies: three traffic-related anomalies (lane blockage and recovery, foreign object intrusion, and sustained congestion) and one sensor-related anomaly (camera angle shift). Our multi-branch detection system integrates deep learning, rule-based logic, and machine learning to improve robustness and precision. Extensive experiments demonstrate that our framework outperforms state-of-the-art methods in precision, recall, and F1-score, providing a cost-effective and scalable solution for real-world intelligent transportation systems.

eess.IV↗

arXiv2025

Random Turán and counting results for general position sets over finite fields

Let $α(\mathbb{F}_q^d,p)$ denote the maximum size of a general position set in a $p$-random subset of $\mathbb{F}_q^d$. We determine the order of magnitude of $α(\mathbb{F}_q^2,p)$ up to polylogarithmic factors for all possible values of $p$, improving the previous results obtained by Roche-Newton--Warren and Bhowmick--Roche-Newton. For $d \ge 3$ we prove upper bounds for $α(\mathbb{F}_q^d,p)$ that are essentially tight within certain ranges for $p$. We establish the upper bound $2^{(1+o(1))q}$ for the number of general position sets in $\mathbb{F}_q^d$, which matches the trivial lower bound $2^{q}$ asymptotically in the exponent. We also refine this counting result by proving an asymptotically tight (in the exponent) upper bound for the number of general position sets with a fixed size. The latter result for $d=2$ improves a result of Roche-Newton--Warren. Our proofs are grounded in the hypergraph container method, and additionally, for $d=2$ we also leverage the pseudorandomness of the point-line incidence graph of $\mathbb{F}_{q}^2$.

math.CO↗