An Efficient Algorithm for Enumerating Chordal Bipartite Induced Subgraphs in Sparse Graphs

Abstract

In this paper, we propose a characterization of chordal bipartite graphs and an efficient enumeration algorithm for chordal bipartite induced subgraphs. A chordal bipartite graph is a bipartite graph without induced cycles with length six or more. It is known that the incident graph of a hypergraph is chordal bipartite graph if and only if the hypergraph is β-acyclic. As the main result of our paper, we show that a graph G is chordal bipartite if and only if there is a special vertex elimination ordering for G, called CBEO. Moreover, we propose an algorithm ECB which enumerates all chordal bipartite induced subgraphs in O(kt∆ 2 ) time per solution on average, where k is the degeneracy, t is the maximum size of Kt,t as an induced subgraph, and ∆ is the degree. ECB achieves constant amortized time enumeration for bounded degree graphs.