TY - GEN
T1 - On Two Variants of Induced Matchings
AU - Chaudhary, Juhi
AU - Panda, B. S.
N1 - Publisher Copyright:
© 2022, The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
PY - 2022/1/1
Y1 - 2022/1/1
N2 - A matching M in a graph G is an induced matching if the subgraph of G induced by M is the same as the subgraph of G induced by S= { v∈ V(G) ∣ v is incident on an edge of M}. Given a graph G and a positive integer k, Induced Matching asks whether G has an induced matching of cardinality at least k. An induced matching M is maximal if it is not properly contained in any other induced matching of G. Given a graph G, Min-Max-Ind-Matching is the problem of finding a maximal induced matching M in G of minimum cardinality. Given a bipartite graph G= (X⊎ Y, E(G) ), Saturated Induced Matching asks whether there exists an induced matching in G that saturates every vertex in Y. In this paper, we study Min-Max-Ind-Matching and Saturated Induced Matching. First, we strengthen the hardness result of Min-Max-Ind-Matching by showing that its decision version remains NP -complete for perfect elimination bipartite graphs, star-convex bipartite graphs, and dually chordal graphs. Then, we show the hardness difference between Induced Matching and Min-Max-Ind-Matching. Finally, we propose a linear-time algorithm to solve Saturated Induced Matching.
AB - A matching M in a graph G is an induced matching if the subgraph of G induced by M is the same as the subgraph of G induced by S= { v∈ V(G) ∣ v is incident on an edge of M}. Given a graph G and a positive integer k, Induced Matching asks whether G has an induced matching of cardinality at least k. An induced matching M is maximal if it is not properly contained in any other induced matching of G. Given a graph G, Min-Max-Ind-Matching is the problem of finding a maximal induced matching M in G of minimum cardinality. Given a bipartite graph G= (X⊎ Y, E(G) ), Saturated Induced Matching asks whether there exists an induced matching in G that saturates every vertex in Y. In this paper, we study Min-Max-Ind-Matching and Saturated Induced Matching. First, we strengthen the hardness result of Min-Max-Ind-Matching by showing that its decision version remains NP -complete for perfect elimination bipartite graphs, star-convex bipartite graphs, and dually chordal graphs. Then, we show the hardness difference between Induced Matching and Min-Max-Ind-Matching. Finally, we propose a linear-time algorithm to solve Saturated Induced Matching.
KW - Induced matching
KW - Linear-time algorithm
KW - Matching
KW - Minimum maximal induced matching
KW - NP -completeness
UR - https://www.scopus.com/pages/publications/85150989812
U2 - 10.1007/978-981-19-9582-8_4
DO - 10.1007/978-981-19-9582-8_4
M3 - Conference contribution
AN - SCOPUS:85150989812
SN - 9789811995811
T3 - Communications in Computer and Information Science
SP - 37
EP - 48
BT - New Trends in Computer Technologies and Applications - 25th International Computer Symposium, ICS 2022, Proceedings
A2 - Hsieh, Sun-Yuan
A2 - Hung, Ling-Ju
A2 - Peng, Sheng-Lung
A2 - Klasing, Ralf
A2 - Lee, Chia-Wei
PB - Springer Science and Business Media Deutschland GmbH
T2 - 25th International Computer Symposium on New Trends in Computer Technologies and Applications, ICS 2022
Y2 - 15 December 2022 through 17 December 2022
ER -