Geodesic
Chromatic Properties of the Pancake Graphs
Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 777-787

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Chromatic properties of the Pancake graphs Pn, n ⩾ 2, that are Cayley graphs on the symmetric group Symn generated by prefix-reversals are investigated in the paper. It is proved that for any n ⩾ 3 the total chromatic number of Pn is n, and it is shown that the chromatic index of Pn is n − 1. We present upper bounds on the chromatic number of the Pancake graphs Pn, which improve Brooks’ bound for n ⩾ 7 and Katlin’s bound for n ⩽ 28. Algorithms of a total n-coloring and a proper (n − 1)-coloring are given.
Keywords: Pancake graph, Cayley graphs, symmetric group, chromatic number, total chromatic number 
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     author = {Konstantinova, Elena},
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Konstantinova, Elena. Chromatic Properties of the Pancake Graphs. Discussiones Mathematicae. Graph Theory, Tome 37 (2017) no. 3, pp. 777-787. http://geodesic.mathdoc.fr/item/DMGT_2017_37_3_a18/