Chromatic Properties of the Pancake Graphs
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 pre...
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| Format: | Article |
| Language: | English |
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Sciendo
2017-08-01
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| Series: | Discussiones Mathematicae Graph Theory |
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| Online Access: | http://www.degruyter.com/view/j/dmgt.2017.37.issue-3/dmgt.1978/dmgt.1978.xml?format=INT |
| Summary: | 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. |
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| ISSN: | 2083-5892 |