Dominating induced matching in some subclasses of bipartite graphs

B. S. Panda, Juhi Chaudhary

Research output: Contribution to journalArticlepeer-review


A subset M⊆E of edges of a graph G=(V,E) is called a matching if no two edges of M share a common vertex. An edge e∈E is said to dominate itself and all other edges adjacent to it. A matching M in a graph G=(V,E) is called a dominating induced matching (d.i.m.) if every edge of G is dominated by edges of M exactly once. The dominating induced matching decide (DIM-DECIDE) problem asks whether a graph G contains a dominating induced matching. The dominating induced matching (DIM) problem asks to compute a dominating induced matching (d.i.m.) in a graph G that admits a dominating induced matching. The DIM-DECIDE problem is known to be NP-complete for general graphs as well as for bipartite graphs. In this paper, we strengthen the NP-completeness result of the DIM-DECIDE problem by showing that this problem remains NP-complete for perfect elimination bipartite graphs, a proper subclass of bipartite graphs. On the positive side, we characterize the class of star-convex bipartite graphs admitting a d.i.m. This characterization leads to a linear time algorithm to test whether a star-convex bipartite graph admits a d.i.m. and, if so, constructs a d.i.m. in such a star-convex bipartite graph in linear time. We also propose polynomial time algorithms to construct a d.i.m. in long-k-star-convex bipartite graphs as well as in circular-convex bipartite graphs if the input graph admits a d.i.m.

Original languageEnglish
Pages (from-to)104-115
Number of pages12
JournalTheoretical Computer Science
StatePublished - 11 Sep 2021
Externally publishedYes


  • Bipartite graphs
  • Dominating induced matching
  • NP-completeness
  • Perfect elimination bipartite graphs
  • Polynomial time algorithms

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science (all)


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