The chromatic number of {ISK4, diamond, bowtie}‐free graphs
Guantao Chen, Yuan Chen, Qing Cui, Xing Feng, Qinghai Liu · Journal of Graph Theory · 2020
Abstract A graph is said to be ‐free if it does not contain any subdivision of as an induced subgraph. Lévêque, Maffray and Trotignon conjectured that every ‐free graph is 4‐colorable. In this paper, we show that this conjecture is true for the class of {, diamond, bowtie}‐free graphs, where a diamond is the graph obtained from by removing one edge and a bowtie is the graph consisting of two triangles with one vertex identified.