• Corpus ID: 119324334

The coloring of the regular graph of ideals

@article{Shaveisi2015TheCO,
  title={The coloring of the regular graph of ideals},
  author={Farzad Shaveisi},
  journal={arXiv: Combinatorics},
  year={2015}
}
  • F. Shaveisi
  • Published 2 January 2015
  • Mathematics
  • arXiv: Combinatorics
The regular graph of ideals of the commutative ring $R$, denoted by $\Gamma_{reg}(R)$, is a graph whose vertex set is the set of all non-trivial ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent if and only if either $I$ contains a $J$-regular element or $J$ contains an $I$-regular element. In this paper, it is shown that for every Artinian ring $R$, the edge chromatic number of $\Gamma_{reg}(R)$ equals its maximum degree. Then a formula for the clique number of $\Gamma_{reg}(R… 

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