Coloring of graphs associated to zero-divisors
| dc.creator | Wang, Hsin-Ju | |
| dc.date | 2007-03-02 | |
| dc.date.accessioned | 2026-07-07T07:49:53Z | |
| dc.date.available | 2026-07-07T07:49:53Z | |
| dc.description | Let $G$ be a graph, $χ(G)$ be the minimal number of colors which can be assigned to the vertices of $G$ in such a way that every two adjacent vertices have different colors and $ω(G)$ to be the least upper bound of the size of the complete subgraphs contained in $G$. It is well-known that $χ(G)\geq ω(G)$. Beck in \cite{b} conjectured that $χ(Γ_0(R))=ω(Γ_0(R))$ if $ω(Γ_0(R))<\infty$, where $Γ_0(R)$ is a graph associated to a commutative ring $R$. In this note, we provide some sufficient conditions for a ring $R$ to enjoy $χ(Γ_0(R))=ω(Γ_0(R))$. As a consequence, we verify Beck's conjecture for the homomorphic image of $\mathbb{Z}^n$. | |
| dc.description | 13 pages | |
| dc.identifier | https://arxiv.org/abs/math/0703051 | |
| dc.identifier | http://arxiv.org/abs/math/0703051 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/124987 | |
| dc.subject | Commutative Algebra | |
| dc.subject | 13A99, 05C15 | |
| dc.title | Coloring of graphs associated to zero-divisors | |
| dc.type | text |