A sufficient condition for the bicolorability of a hypergraph

In this note we prove a long-standing conjecture of Sterboul [P. Duchet, Hypergraphs, in: R. Graham, M. Grötschel, L. Lovász (Eds.), Handbook of Combinatorics, 1995, pp. 381–432 (Chapter 7)], which states that a hypergraph is bicolorable provided it does not contain a specific kind of odd cycle. This is currently the strongest result of its kind, improving on results by Berge [Graphs and Hypergraphs, North-Holland, American Elsevier, Amsterdam, 1973] and Fournier and Las Vergnas [Une classe d’hypergraphes bichromatiques II, Discrete Math. 7 (1974) 99–106; A class of bichromatic hypergraphs, Ann. Discrete Math. 21, in: C. Berge, V. Chvátal (Eds.), Topics on Perfect Graphs, 1984, pp. 21–27].