We present an algorithm for determining whether a bipartite graph $G$ is 2-chordal (formerly doubly chordal bipartite). At its core this algorithm is an extension of the existing efficient algorithm for determining whether a graph is chordal bipartite. We then introduce the notion of $k$-chordal bipartite graphs and show by inductive means that a slight modification of our algorithm is sufficient to detect this property. We show that there are no nontrivial $k$-chordal bipartite graphs for $k \geq 4$ and that both the 2-chordal bipartite and 3-chordal bipartite problem are contained within complexity class P.

翻译：我们提出一种算法,用以确定双方图形$G$是否为2和2之和(前为2和2之和) 。 就其核心而言,这一算法是现有有效算法的延伸,用以确定一个图形是否为chodal 双巴。 然后我们引入了 $k$-chodal 双巴图的概念,并通过感想来显示我们算法的略微修改足以检测这一属性。 我们显示,对于 $k\ geq 4 来说, 不存在非三方 $k$k$k-chodal 双方图, 2和 3-chodal 双方图的问题都包含在复杂的 P 类中 。