We show that attaching a whisker (or a pendant) at the vertices of a cycle cover of a graph results in a new graph with the following property: all symbolic powers of its cover ideal are Koszul or, equivalently, componentwise linear. This extends previous work where the whiskers were added to all vertices or to the vertices of a vertex cover of the graph.

中文翻译：

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图的覆盖理想的符号权力和 Koszul 财产

我们表明，在图的循环覆盖的顶点处附加晶须（或垂饰）会产生具有以下属性的新图：其覆盖理想的所有符号幂都是 Koszul 或等效的分量线性。这扩展了之前的工作，其中胡须被添加到所有顶点或图的顶点覆盖的顶点。