On the ratio between maximum weight perfect matchings and maximum weight matchings in grids

@article{Fonseca2016OnTR,
  title={On the ratio between maximum weight perfect matchings and maximum weight matchings in grids},
  author={Guilherme Dias da Fonseca and Bernard Ries and Diana Sasaki},
  journal={Discrete Applied Mathematics},
  year={2016},
  volume={207},
  pages={45-55}
}
Given a graph G that admits a perfect matching, we investigate the parameter η(G) (originally motivated by computer graphics applications) which is defined as follows. Among all nonnegative edge weight assignments, η(G) is the minimum ratio between (i) the maximum weight of a perfect matching and (ii) the maximum weight of a general matching. In this paper, we determine the exact value of η for all rectangular grids, all bipartite cylindrical grids, and all bipartite toroidal grids. We… CONTINUE READING