Martinsson-Steiner Conjecture on Fractional Chromatic Number
Prior state unknown→proved
girth >= 5 case; the triangle-free case remains open
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combinatorics / Graph coloring
Martinsson-Steiner Conjecture on Fractional Chromatic Number
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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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.
girth >= 5 case; the triangle-free case remains open
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