Efficient Algorithm for Checking 2-Chordal (Doubly Chordal) Bipartite Graphs

04/12/2021

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by   Austin Alderete, et al.

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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 ≥ 4 and that both the 2-chordal bipartite and 3-chordal bipartite problem are contained within complexity class P.