Coloring graphs with no induced five-vertex path or gem
Journal of Graph Theory
For a graph (Formula presented.), let (Formula presented.) and (Formula presented.), respectively, denote the chromatic number and clique number of (Formula presented.). We give an explicit structural description of ((Formula presented.), gem)-free graphs, and show that every such graph (Formula presented.) satisfies (Formula presented.). Moreover, this bound is best possible. Here a gem is the graph that consists of an induced four-vertex path plus a vertex which is adjacent to all the vertices of that path.
Chudnovsky, Maria; Karthick, T.; Maceli, Peter; and Maffray, Frédéric, "Coloring graphs with no induced five-vertex path or gem" (2020). Journal Articles. 56.