A k-tree is either a complete graph on k vertices or a graph that contains a vertex whose neighborhood induces a complete graph on k vertices and whose removal results in a k-tree. If the comparability graph of a poset P is a k-tree, we say that P is a k-tree poset. In the present work, we study and characterize by forbidden subposets the k-tree posets that admit a containment model mapping vertices into paths of a tree (CPT k-tree posets). Furthermore, we characterize the dually-CPT and strong-CPT k-tree posets and their comparability graphs. The characterizations lead to efficient recognition algorithms for the respective classes.

中文翻译：

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关于树中路径的k树包含图

甲ķ -tree要么是上一个完全图ķ顶点或包含其顶点附近诱导上的完全图的曲线图ķ顶点和其脱除导致ķ -tree。如果位姿P的可比性图是k树，则说P是k树位。在目前的工作中，我们研究并禁止subposets的表征ķ -树偏序集是认错遏制模型映射顶点成一棵树（路径CPT ķ -树偏序集）。此外，我们描述了双重CPT和强CPT k树姿势及其可比性图。表征导致针对各个类别的有效识别算法。