MathConstraint generates scalable, automatically verifiable combinatorial problems where LLMs achieve 18.5-66.9% accuracy without tools but roughly double that with solver access.
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8 Pith papers cite this work, alongside 1,928 external citations. Polarity classification is still indexing.
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Proves the Dallard et al. conjecture holds for outerstring graphs and sharpens bounds on tree-independence number for multiple K_{1,d}-free classes.
Verifies stronger coarse balanced separator conjecture for all r in K_{t,t}-induced-minor-free graphs of bounded clique number via a polynomial-size hitting set Z for large balls on any Y.
Proves that graphs on N ≥ 2n vertices with δ(G) ≥ ⌊3N/4⌋ have every 2-edge-coloring containing a monochromatic copy of every n-vertex tree with max degree ≤ Δ.
A SAT-plus-LLM method discovers infinite families of doubly saturated Ramsey-good graphs, answering Grinstead and Roberts' 1982 question.
Authors compute new small two-color ordered and cyclic Ramsey numbers for monotone paths, cycles, stars, complete graphs and nested matchings via SAT solving, determine closed forms for several pairs of graph classes, obtain bounds, apply reinforcement learning for lower bounds, and introduce permut
SAT-based computation yields exact small reflective and dihedral Ramsey numbers for several ordered graph families, plus closed formulas and conjectures linking them to ordered and cyclic variants.
The paper overviews universal obstructions as a unifying framework for graph parameters, surveys existing results across many parameters, and offers some unifying classification results.
citing papers explorer
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MathConstraint: Automated Generation of Verified Combinatorial Reasoning Instances for LLMs
MathConstraint generates scalable, automatically verifiable combinatorial problems where LLMs achieve 18.5-66.9% accuracy without tools but roughly double that with solver access.
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Tree-independence number of $K_{1,d}$-free graph classes
Proves the Dallard et al. conjecture holds for outerstring graphs and sharpens bounds on tree-independence number for multiple K_{1,d}-free classes.
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Coarse Balanced Separators in Biclique-Induced-Minor-Free Graphs
Verifies stronger coarse balanced separator conjecture for all r in K_{t,t}-induced-minor-free graphs of bounded clique number via a polynomial-size hitting set Z for large balls on any Y.
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A degree version of the Burr-Erd\H{o}s conjecture on trees
Proves that graphs on N ≥ 2n vertices with δ(G) ≥ ⌊3N/4⌋ have every 2-edge-coloring containing a monochromatic copy of every n-vertex tree with max degree ≤ Δ.
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Doubly Saturated Ramsey Graphs: A Case Study in Computer-Assisted Mathematical Discovery
A SAT-plus-LLM method discovers infinite families of doubly saturated Ramsey-good graphs, answering Grinstead and Roberts' 1982 question.
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Some results on small ordered and cyclic Ramsey numbers
Authors compute new small two-color ordered and cyclic Ramsey numbers for monotone paths, cycles, stars, complete graphs and nested matchings via SAT solving, determine closed forms for several pairs of graph classes, obtain bounds, apply reinforcement learning for lower bounds, and introduce permut
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Computation of small reflective and dihedral Ramsey numbers
SAT-based computation yields exact small reflective and dihedral Ramsey numbers for several ordered graph families, plus closed formulas and conjectures linking them to ordered and cyclic variants.
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An Overview of Universal Obstructions for Graph Parameters
The paper overviews universal obstructions as a unifying framework for graph parameters, surveys existing results across many parameters, and offers some unifying classification results.