Bruhn–Fuchs characterization of t‑perfection via fractional chromatic numbers of t‑minors

Characterize the class of t‑perfect graphs by proving that a graph G is t‑perfect if and only if, for every non‑bipartite t‑minor H of G, the fractional chromatic number satisfies χ*(H) = 2 + 2/(oddgirth(H) − 1).

Background

The paper reviews fractional chromatic bounds for t‑perfect graphs and notes that one direction of a proposed characterization follows readily from these bounds. Bruhn and Fuchs conjectured a full equivalence linking t‑perfection to a precise fractional chromatic formula applied to all non‑bipartite t‑minors. The authors include this conjecture to situate their results within broader efforts to characterize t‑perfection.