Maximum weight induced matching in some subclasses of bipartite graphs

B. S. Panda, Arti Pandey, Juhi Chaudhary, Piyush Dane, Manav Kashyap

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

A subset M⊆ E of edges of a graph G= (V, 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 the same as G[S], the subgraph of G induced by S= { v∈ V| v is incident on an edge of M}. The Maximum Induced Matching problem is to find an induced matching of maximum cardinality. Given a graph G and a positive integer k, the Induced Matching Decision problem is to decide whether G has an induced matching of cardinality at least k. The Maximum Weight Induced Matching problem in a weighted graph G= (V, E) in which the weight of each edge is a positive real number, is to find an induced matching such that the sum of the weights of its edges is maximum. It is known that the Induced Matching Decision problem and hence the Maximum Weight Induced Matching problem is known to be NP-complete for general graphs and bipartite graphs. In this paper, we strengthened this result by showing that the Induced Matching Decision problem is NP-complete for star-convex bipartite graphs, comb-convex bipartite graphs, and perfect elimination bipartite graphs, the subclasses of the class of bipartite graphs. On the positive side, we propose polynomial time algorithms for the Maximum Weight Induced Matching problem for circular-convex bipartite graphs and triad-convex bipartite graphs by making polynomial time reductions from the Maximum Weight Induced Matching problem in these graph classes to the Maximum Weight Induced Matching problem in convex bipartite graphs.

Original languageEnglish
Pages (from-to)713-732
Number of pages20
JournalJournal of Combinatorial Optimization
Volume40
Issue number3
DOIs
StatePublished - 1 Oct 2020
Externally publishedYes

Keywords

  • Bipartite graphs
  • Graph algorithm
  • Induced matching
  • Matching
  • NP-complete

ASJC Scopus subject areas

  • Computer Science Applications
  • Discrete Mathematics and Combinatorics
  • Control and Optimization
  • Computational Theory and Mathematics
  • Applied Mathematics

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