Coloring the power graph of a semigroup

Yaroslav Shitov

Coloring the power graph of a semigroup

Combinatorics 2016-07-05 v1

Authors: Yaroslav Shitov

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.

Keywords

power graph semigroup chromatic number graph coloring countable adjacency

Cite

@article{arxiv.1607.00420,
  title  = {Coloring the power graph of a semigroup},
  author = {Yaroslav Shitov},
  journal= {arXiv preprint arXiv:1607.00420},
  year   = {2016}
}

Comments

note, 4 pages

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