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Glauco Rampone

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Preprint Aug 2026

Improved bounds for the smallest 4-chromatic graph of girth six

For integers $k,g \ge 3$ let $n_g(k)$ denote the minimum order of a graph with chromatic number $k$ and girth at least $g$. Exoo and Goedgebeur (DMTCS 2019) proved $26 \le n_6(4) \le 66$; their 66-vertex witness has remained the smallest known 4-chromatic graph of girth 6. We improve both bounds to $29 \le n_6(4) \le 6...

Glauco Rampone · 0 citations