Abstract
Let G be a semigroup. The vertices of the power graph \({\mathcal {P}}(G)\) are the elements of G, and two elements are adjacent if and only if one of them is a power of the other. We show that the chromatic number of \({\mathcal {P}}(G)\) is at most countable, answering a recent question of Aalipour et al.
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Aalipour, G., Akbari, S., Cameron, P.J., Nikandish, R., Shaveisi, F.: On the structure of the power graph and the enhanced power graph of a group. (2016) (preprint ) arXiv:1603.04337
Cameron, P.J.: The power graph of a finite group, II. J. Group Theory 13, 779–783 (2010)
Cameron, P.J., Ghosh, S.: The power graph of a finite group. Discrete Math. 311, 1220–1222 (2011)
Fodor, G.: Proof of a conjecture of P. Erdős. Acta Sci. Math. Hung 14, 219–227 (1952)
Komjáth, P.: A note on uncountable chordal graphs. Discrete Math. 338, 1565–1566 (2015)
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Shitov, Y. Coloring the Power Graph of a Semigroup. Graphs and Combinatorics 33, 485–487 (2017). https://doi.org/10.1007/s00373-017-1773-8
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DOI: https://doi.org/10.1007/s00373-017-1773-8