Diverse Pairs of Matchings
Abstract
We initiate the study of the Diverse Pair of (Maximum/ Perfect) Matchings problems which given a graph $G$ and an integer $k$, ask whether $G$ has two (maximum/perfect) matchings whose symmetric difference is at least $k$. Diverse Pair of Matchings (asking for two not necessarily maximum or perfect matchings) is NP-complete on general graphs if $k$ is part of the input, and we consider two restricted variants. First, we show that on bipartite graphs, the problem is polynomial-time solvable, and second we show that Diverse Pair of Maximum Matchings is FPT parameterized by $k$. We round off the work by showing that Diverse Pair of Matchings has a kernel on $\mathcal{O}(k^2)$ vertices.
- Publication:
-
arXiv e-prints
- Pub Date:
- September 2020
- DOI:
- 10.48550/arXiv.2009.04567
- arXiv:
- arXiv:2009.04567
- Bibcode:
- 2020arXiv200904567F
- Keywords:
-
- Computer Science - Data Structures and Algorithms;
- 05C85;
- F.2.2;
- G.2.2
- E-Print:
- To appear at ISAAC 2020