Clique-node and closed neighborhood matrices of circular interval graphs are circular matrices. The stable set polytope and the dominating set polytope on these graphs are therefore closely related to the set packing polytope and the set covering polyhedron on circular matrices. Eisenbrand et al. (2008) take advantage of this relationship to propose a complete linear description of the stable set polytope on circular interval graphs. In this paper we follow similar ideas to obtain a complete description of the dominating set polytope on the same class of graphs. As in the packing case, our results are established for a larger class of covering polyhedra of the form $Q^{\ast }(A,b)≔\mathrm{conv}\left\{x\in {\mathbb{Z}}_{+}^n:Ax\ge b\right\}$, with $A$ a circular matrix and $b$ an integer vector. These results also provide linear descriptions of polyhedra associated with several variants of the dominating set problem on circular interval graphs.

圆形间隔图的集团节点和封闭邻域矩阵是圆形矩阵。因此，这些图上的稳定变位多面体和占优势的变位多面体与圆形矩阵上的变位堆积多面体和变位覆盖多面体密切相关。Eisenbrand等。（2008）利用这种关系来提出圆形区间图上的稳定集多面体的完整线性描述。在本文中，我们遵循类似的想法，以获取对同一类图上支配集多边形的完整描述。与包装情况一样，我们的结果适用于以下形式的更大范围的覆盖多面体${问}^{\ast }（\mathrm{一种}，b）≔\mathrm{转换}\left\{X\in {\mathbb{ž}}_{+}^{ñ}：\mathrm{一种}X\ge b\right\}$，带有 $\mathrm{一种}$ 圆矩阵和 $b$整数向量。这些结果还提供了与多面体相关的线性描述，这些多面体与圆形区间图上支配集问题的几种变体相关。