Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 24 November 2020Accepted: 25 July 2021Published online: 23 2021Keywordsgraphs, fractional coloring, girth, triangle-free, RamseyAMS Subject Headings05C15Publication DataISSN (print): 0895-4801ISSN (online): 1095-7146Publisher: Society for Industrial and Applied Mathematic...

Resolving a problem raised by Norin in 2020, we show that for each k ? N $k \in \mathbb {N}$ , the minimal f ( ) $f(k) with property every graph G $G$ chromatic number at least + 1 $f(k)+1$ contains subgraph H $H$ both connectivity and $k$ satisfies ? 7 \leqslant 7k$ . This result is best-possible up to multiplicative constants, sharpens earlier results of Alon–Kleitman–Thomassen–Saks–Seymour f...