An r-partite graph is an interval r-graph if corresponding to each vertex we can assign an interval of the real line such that two vertices u and v of different partite sets are adjacent if and only if their corresponding intervals intersect. In this paper, we provide two vertex-ordering characterizations of interval r-graphs and identify forbidden patterns for interval r-graphs in terms of specific orderings of their vertices.

翻译：若一个r部图是区间r图，则对应于每个顶点，我们可以分配一个实数轴上的区间，使得来自不同部集的两个顶点u和v相邻当且仅当它们对应的区间相交。本文中，我们给出了区间r图的两个顶点序刻画，并通过其顶点的特定排序模式识别了区间r图的禁止模式。