Abstract
The maximum stable matching problem (Max-SMP) and the minimum stable matching problem (Min-SMP) have been known to be NP-hard for subcubic bipartite graphs, while Max-SMP can be solved in polynomal time for a bipartite graph G with a bipartition such that \mathrm{deg}:{G}(v)\le 2 for any v\in X. This paper shows that both Max-SMP and Min-SMP can be solved in linear time for trees. This is the first polynomially solvable case for Min-SMP, as far as the authors know. We also consider some extensions to the case when G is a general/bipartite graph with edge weights.
Cite
CITATION STYLE
Tayu, S., & Ueno, S. (2017). Stable Matchings in Trees. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10392 LNCS, pp. 492–503). Springer Verlag. https://doi.org/10.1007/978-3-319-62389-4_41
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