For each integer n ≥ 7, we exhibit graphs of chromatic number n that contain no subdivided Kn as a subgraph. However, we show that a graph with chromatic number 4 contains as a subgraph a subdivided K4 in which each triangle of the K4 is subdivided to form an odd cycle. © 1979.
Catlin, P. A. (1979). Hajós’ graph-coloring conjecture: Variations and counterexamples. Journal of Combinatorial Theory, Series B, 26(2), 268–274. https://doi.org/10.1016/0095-8956(79)90062-5