A paired-dominating set of a graph G is a dominating set D with the additional requirement that the induced subgraph G[D] contains a perfect matching. We prove that the vertex set of every claw-free cubic graph can be partitioned into two paired-dominating sets.

中文翻译：

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三次图中的不相交的配对控制集。

图G的成对支配集是支配集D，其附加要求是诱导子图G [D]包含完美匹配。我们证明了每个无爪三次图的顶点集都可以划分为两个成对的主导集。