Abstract

We provide a general framework on the coefficients of the graph polynomials of graphs which are Cartesian products. As a corollary, we prove that if $G=\left(V,E\right)$ is a graph with degrees of vertices $2d\left(v\right)$, $v\in V$, and the graph polynomial ${\prod }_{\left(i,j\right)\in E}\left(x_j-x_i\right)$ contains an “almost central” monomial (that is a monomial ${\prod }_v{x}_v^{c_v}$, where $|c_v-d\left(v\right)|\le 1$ for all $v\in V$), then the Cartesian product $G\square C_{2n}$ is $\left(d\left(\cdot \right)+2\right)$-choosable.

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