TY - GEN

T1 - Parameterized Results on Acyclic Matchings with Implications for Related Problems

AU - Chaudhary, Juhi

AU - Zehavi, Meirav

N1 - Publisher Copyright:
© 2023, The Author(s), under exclusive license to Springer Nature Switzerland AG.

PY - 2023/1/1

Y1 - 2023/1/1

N2 - A matching M in a graph G is an acyclic matching if the subgraph of G induced by the endpoints of the edges of M is a forest. Given a graph G and a positive integer l, Acyclic Matching asks whether G has an acyclic matching of size (i.e., the number of edges) at least l. In this paper, we first prove that assuming (Formula presented), there does not exist any FPT-approximation algorithm for Acyclic Matching that approximates it within a constant factor when parameterized by l. Our reduction is general in the sense that it also asserts FPT-inapproximability for Induced Matching and Uniquely Restricted Matching. We also consider three below-guarantee parameters for Acyclic Matching, viz. (Formula presented), where n is the number of vertices in G, MM(G) is the matching number of G, and IS(G) is the independence number of G. We note that the result concerning the below-guarantee parameter n/2-l is the most technical part of our paper. Also, we show that Acyclic Matching does not exhibit a polynomial kernel with respect to vertex cover number (or vertex deletion distance to clique) plus the size of the matching unless (Formula presented).

AB - A matching M in a graph G is an acyclic matching if the subgraph of G induced by the endpoints of the edges of M is a forest. Given a graph G and a positive integer l, Acyclic Matching asks whether G has an acyclic matching of size (i.e., the number of edges) at least l. In this paper, we first prove that assuming (Formula presented), there does not exist any FPT-approximation algorithm for Acyclic Matching that approximates it within a constant factor when parameterized by l. Our reduction is general in the sense that it also asserts FPT-inapproximability for Induced Matching and Uniquely Restricted Matching. We also consider three below-guarantee parameters for Acyclic Matching, viz. (Formula presented), where n is the number of vertices in G, MM(G) is the matching number of G, and IS(G) is the independence number of G. We note that the result concerning the below-guarantee parameter n/2-l is the most technical part of our paper. Also, we show that Acyclic Matching does not exhibit a polynomial kernel with respect to vertex cover number (or vertex deletion distance to clique) plus the size of the matching unless (Formula presented).

KW - Acyclic Matching

KW - Induced Matching

KW - Kernelization Lower Bounds

KW - Parameterized Algorithms

KW - Uniquely Restricted Matching

UR - http://www.scopus.com/inward/record.url?scp=85174525904&partnerID=8YFLogxK

U2 - 10.1007/978-3-031-43380-1_15

DO - 10.1007/978-3-031-43380-1_15

M3 - Conference contribution

AN - SCOPUS:85174525904

SN - 9783031433795

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

SP - 201

EP - 216

BT - Graph-Theoretic Concepts in Computer Science - 49th International Workshop, WG 2023, Revised Selected Papers

A2 - Paulusma, Daniël

A2 - Ries, Bernard

PB - Springer Science and Business Media Deutschland GmbH

T2 - 49th International Workshop on Graph-Theoretic Concepts in Computer Science, WG 2023

Y2 - 28 June 2023 through 30 June 2023

ER -