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-部图满足：存在一个从每个顶点到实数轴上一个区间的对应关系，使得两个属于不同部集的顶点u和v相邻当且仅当它们对应的区间相交，则称该图为区间r-图。本文给出了区间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-图的禁止结构。