# GTBench: A Curriculum-Grounded Benchmark for Evaluating LLMs as Mathematical Research Assistants in Graph Theory

arXiv: https://arxiv.org/abs/2606.03144 · HTML: https://mlsanity.com/paper/2606.03144/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 18 of its 32 references that are in the map.
- First posted on arXiv 2 Jun 2026.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 18 of 18)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Judging LLM-as-a-Judge with MT-Bench and Chatbot Arena](https://mlsanity.com/paper/2306.05685/) (2023)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [Mathematical Capabilities of ChatGPT](https://mlsanity.com/paper/2301.13867/) (2023)
- [Can Language Models Solve Graph Problems in Natural Language?](https://mlsanity.com/paper/2305.10037/) (2023)
- [FrontierMath: A Benchmark for Evaluating Advanced Mathematical Reasoning in AI](https://mlsanity.com/paper/2411.04872/) (2024)
- [CombiBench: Benchmarking LLM Capability for Combinatorial Mathematics](https://mlsanity.com/paper/2505.03171/) (2025)
- [CoRe: Benchmarking LLMs Code Reasoning Capabilities through Static Analysis Tasks](https://mlsanity.com/paper/2507.05269/) (2025)
- [LemmaBench: A Live, Research-Level Benchmark to Evaluate LLM Capabilities in Mathematics](https://mlsanity.com/paper/2602.24173/) (2026)
- [LLM & HPC:Benchmarking DeepSeek's Performance in High-Performance Computing Tasks](https://mlsanity.com/paper/2504.03665/) (2025)
- [Evaluating AI-generated code for C++, Fortran, Go, Java, Julia, Matlab, Python, R, and Rust](https://mlsanity.com/paper/2405.13101/) (2024)
- [LLM Benchmarking with LLaMA2: Evaluating Code Development Performance Across Multiple Programming Languages](https://mlsanity.com/paper/2503.19217/) (2025)
- [Can LLMs Find Bugs in Code? An Evaluation from Beginner Errors to Security Vulnerabilities in Python and C++](https://mlsanity.com/paper/2508.16419/) (2025)
- [LLM-HPC++: Evaluating LLM-Generated Modern C++ and MPI+OpenMP Codes for Scalable Mandelbrot Set Computation](https://mlsanity.com/paper/2512.17023/) (2025)
- [Evaluating Large Language Models on Solved and Unsolved Problems in Graph Theory: Implications for Computing Education](https://mlsanity.com/paper/2602.05059/) (2026)

## Built on by (most cited first, 1 of 1)

- [AutoGraphForge: Towards Automated Graph Theory Discovery](https://mlsanity.com/paper/2609.03478/) (2026)

## Abstract (arXiv)

Large language models (LLMs) are increasingly used as self-study assistants in technical disciplines, yet their reliability as mathematical reasoning assistants remains poorly understood. We introduce GTBench, a curriculum-grounded benchmark for evaluating LLMs as mathematical research assistants in graph theory, comprising 63 problems organized into three groups of increasing difficulty: undergraduate definitions and basic properties (Group 1), algorithm tracing and structural reasoning (Group 2), and graduate-level proof construction (Group 3). Problems are sourced from verified academic materials including Diestel's Graph Theory. We evaluate five frontier models -- GPT-5, Claude Sonnet 4.6, Gemini 2.5 Flash-Lite, Llama 3.3 70B, and Mistral Large 3 -- under zero-shot and chain-of-thought prompting, using exact-match and LLM-as-judge evaluation for Groups 1 and 2, and a hybrid human expert and LLM-as-judge protocol for Group 3. Our results reveal a pronounced performance hierarchy: GPT-5 approaches ceiling on Group 1 (95.8% zero-shot) and maintains meaningful accuracy on graduate proofs (82%), while all other models degrade substantially with difficulty, with Llama achieving 0% under human evaluation on Group 3 zero-shot. Failure mode analysis shows that correct algorithm, wrong execution errors dominate Groups 1 and 2, while Group 3 additionally surfaces incomplete reasoning failures and reveals systematic disagreement between human evaluators and the automated judge, particularly on verbose or near-complete proofs (kappa = 0.48-0.83 across human pairs). GTBench provides the first curriculum-grounded evaluation framework for graph-theoretic reasoning in LLMs, with direct implications for the governance of AI tools in mathematical education and scientific research.