Triangle-free graphs that do not contain an induced subdivision of $K_4$ are 3-colorable
Maria Chudnovsky, Chun-Hung Liu, Oliver Schaudt, Sophie Spirkl, ·2017-04-26·via math.CO updates on arXiv.org
We show that triangle-free graphs that do not contain an induced subgraph isomorphic to a subdivision of K4 are 3-colorable. This proves a conjecture of Trotignon and Vuskovic.