RamseyGadgets: A Graph Construction Dataset for LLMs

[2608.14999] RamseyGadgets: A Graph Construction Dataset for LLMs Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Computation and Language arXiv:2608.14999 (cs) [Submitted on 15 Aug 2026] Title: RamseyGadgets: A Graph Construction Dataset for LLMs Authors: Zohair Raza Hassan , Deepak Pandita View a PDF of the paper titled RamseyGadgets: A Graph Construction Dataset for LLMs, by Zohair Raza Hassan and 1 other authors View PDF HTML (experimental) Abstract: Constructing special graphs is an important task within graph theory and computer science. Many popular graph constructions are the result of a comprehensive exploration of relevant graphs and human ingenuity. Given the rise of generative AI usage in mathematics, it is natural to test whether LLMs are able to construct graphs with specified properties using their reasoning capabilities. Unfortunately, many natural graph construction problems, such as finding extremal Ramsey-good graphs (i.e., avoiding specific monochromatic subgraphs), have been explored extensively in the literature, making it difficult to ascertain whether a construction is the product of an LLM's reasoning capabilities or its recollection from training data. In this work, we introduce \textbf{RamseyGadgets}, a novel dataset of 70 underexplored graph construction problems that require finding Ramsey-good graphs with special properties (e.g., containing an edge with a fixed color). These problems have reasonably sized solutions (at most 10 vertices) that can be verified by SAT solvers, making them suitable for automatic evaluation. Our dataset is easily expandable, as one can simply change the monochromatic subgraphs being avoided to obtain a new set of problems. We evaluate the performance of five open-source LLMs on our dataset and report the results. Our findings show that LLMs achieve only 37.70% accuracy on the hard-tier problems in our dataset, with Gemma-4-31B achieving the highest performance out of the five. We also showcase how our dataset allows us to ascertain what kind of hints help LLMs perform better at this task. Subjects: Computation and Language (cs.CL) ; Artificial Intelligence (cs.AI) Cite as: arXiv:2608.14999 [cs.CL] (or arXiv:2608.14999v1 [cs.CL] for this version) https://doi.org/10.48550/arXiv.2608.14999 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Deepak Pandita [ view email ] [v1] Sat, 15 Aug 2026 03:15:07 UTC (454 KB) Full-text links: Access Paper: View a PDF of the paper titled RamseyGadgets: A Graph Construction Dataset for LLMs, by Zohair Raza Hassan and 1 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.CL < prev | next > new | recent | 2026-08 Change to browse by: cs cs.AI References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

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