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Dominating Induced Matching in Some Subclasses of Bipartite Graphs

  • B. S. PandaEmail author
  • Juhi Chaudhary
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11394)

Abstract

Given a graph \(G=(V,E)\), a set \(M\subseteq E\) is called a matching in G if no two edges in M share a common vertex. A matching M in G is called an induced matching if G[M], the subgraph of G induced by M, is same as G[S], the subgraph of G induced by \(S=\{v\in V |\) v is incident on an edge of \(M \}\). An induced matching M in a graph G is dominating if every edge not in M shares exactly one of its endpoints with a matched edge. The dominating induced matching (DIM) problem (also known as Efficient Edge Domination) is a decision problem that asks whether a graph G contains a dominating induced matching or not. This problem is NP-complete for general graphs as well as for bipartite graphs. In this paper, we show that the DIM problem is NP-complete for perfect elimination bipartite graphs and propose polynomial time algorithms for star-convex, triad-convex and circular-convex bipartite graphs which are subclasses of bipartite graphs.

Keywords

Matching Dominating induced matching Graph algorithms NP-completeness Polynomial time algorithms 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Computer Science and Application Group, Department of MathematicsIndian Institute of Technology DelhiNew DelhiIndia

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