TY - GEN

T1 - Dominating induced matching in some subclasses of bipartite graphs

AU - Panda, B. S.

AU - Chaudhary, Juhi

N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2019.

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Given a graph G=(V,E), a set (Formula presented) 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 ∈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.

AB - Given a graph G=(V,E), a set (Formula presented) 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 ∈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.

KW - Dominating induced matching

KW - Graph algorithms

KW - Matching

KW - NP-completeness

KW - Polynomial time algorithms

UR - http://www.scopus.com/inward/record.url?scp=85063442062&partnerID=8YFLogxK

U2 - 10.1007/978-3-030-11509-8_12

DO - 10.1007/978-3-030-11509-8_12

M3 - Conference contribution

AN - SCOPUS:85063442062

SN - 9783030115081

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 138

EP - 149

BT - Algorithms and Discrete Applied Mathematics - 5th International Conference, CALDAM 2019, Proceedings

A2 - Vijayakumar, Ambat

A2 - Pal, Sudebkumar Prasant

PB - Springer Verlag

T2 - 5th International Conference on Algorithms and Discrete Applied Mathematics, CALDAM 2019

Y2 - 14 February 2019 through 16 February 2019

ER -