Problem detail · source-aware
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Is the fractional chromatic number of every $d$-degenerate triangle-free graph at most $(1+o(1))\frac{d}{\log d}$, with a matching lower bound, as conjectured by Martinsson and Steiner? The upper bound is confirmed constructively for graphs of girth at least $5$, and the conjectured lower bound is established in a stronger form for every fixed girth; the original triangle-free case remains open.
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The model solved an optimization problem the authors formulated to determine the correct shape of the fractional clique function, checked and simplified probabilistic and algebraic estimates, helped draft some calculations, and pointed the authors to a key reference. The construction and overall strategy are the authors', who take full responsibility.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
arXiv preprint; not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
girth >= 5 case; the triangle-free case remains open
Source-reported tools: argument.
Independent: unknown · difference confidence: 0
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.