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 Vušković.
Maria Chudnovsky, Chun-Hung Liu, Oliver Schaudt, Sophie Spirkl, Nicolas Trotignon, Kristina Vušković
(2019).
Triangle-free graphs that do not contain an induced subdivision of K4 are 3-colorable. UWSpace.
http://hdl.handle.net/10012/18529