On the Chromatic Number of (P6 , Diamond)-Free Graphs
Graphs and Combinatorics
In this paper, we first show that every (P6, diamond, K4)-free graph is 6-colorable. We also give an example of a (P6, diamond, K4)-free graph G with χ(G) = 6. Further, we show that for every (P6, diamond)-free graph G, the chromatic number of G is upper bounded by a linear function of its clique number. This generalizes some known results in the literature.
Karthick, T. and Mishra, Suchismita, "On the Chromatic Number of (P6 , Diamond)-Free Graphs" (2018). Journal Articles. 1324.