AutoGraphForge: Towards Automated Graph Theory Discovery

arXiv:2609.03478 · cs.AI, cs.LO, math.CO · Submitted 2026-09-03 · Read on arXiv

cs.AI, cs.LO, math.CO

Submitted: 2026-09-03

Updated: 2026-09-03

Code: https://github.com/JanPastorek/AutoGraphForge

Terminology

• Core — 5× in this paper · explained in 2 episodes
• Failure Modes — 5× in this paper · explained in 3 episodes
• House of Graphs — 4× in this paper
• Reinforcement Learning — 4× in this paper · explained in 4 episodes
• Deep Reinforcement Learning — 2× in this paper · explained in 2 episodes
• Verification — 2× in this paper · explained in 2 episodes
• Agentic Loop — 1× in this paper · explained in 1 episode
• Axioms — 1× in this paper · explained in 2 episodes
• Benchmark — 1× in this paper · explained in 2 episodes
• Generative AI — 1× in this paper · explained in 2 episodes
• Generative Model — 1× in this paper · explained in 2 episodes
• Redundancy — 1× in this paper · explained in 2 episodes
• SMT solver — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Transformer — 1× in this paper · explained in 2 episodes
• Unified Framework — 1× in this paper · explained in 5 episodes

Sources

• Automated conjecturing with \emph{TxGraffiti}
• The \emph{Optimist}: Towards Fully Automated Graph Theory Research
• PHOEG: an online tool for discovery and education in extremal graph theory
• Computer-assisted graph theory: a survey
• Constructions in combinatorics via neural networks
• Maintaining a Library of Formal Mathematics
• Autoformalization with Large Language Models
• Formalizing chip-firing and Riemann--Roch for graphs in Lean 4
• GTBench: A Curriculum-Grounded Benchmark for Evaluating LLMs as Mathematical Research Assistants in Graph Theory
• An automated proof that R(B_8,B_10)=37
• LeanMarathon: Toward Reliable AI Co-Mathematicians through Long-Horizon Lean Autoformalization
• OProver: A Unified Framework for Agentic Formal Theorem Proving
• RLGT: A reinforcement learning framework for extremal graph theory

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