Geodesic
An improved bound on the chromatic number of the Pancake graphs
Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 1, pp. 35-46

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In this paper, an improved bound on the chromatic number of the Pancake graph P_n, n⩾ 9, is presented. The bound is obtained using a subadditivity property of the chromatic number of the Pancake graph. We also investigate an equitable coloring of P_n. An equitable (n-1)-coloring based on efficient dominating sets is given and optimal equitable 4-colorings are considered for small n. It is conjectured that the chromatic number of P_n coincides with its equitable chromatic number for any n ⩾ 2.
Keywords: Pancake graph, chromatic number, equitable coloring 
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Droogendijk, Leen; Konstantinova, Elena. An improved bound on the chromatic number of the Pancake graphs. Discussiones Mathematicae. Graph Theory, Tome 44 (2024) no. 1, pp. 35-46. http://geodesic.mathdoc.fr/item/DMGT_2024_44_1_a2/