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Counting Maximum Matchings in Planar Graphs Is Hard
arXiv - CS - Computational Complexity Pub Date : 2020-01-06 , DOI: arxiv-2001.01493 Istvan Miklos, Miklos Kresz
arXiv - CS - Computational Complexity Pub Date : 2020-01-06 , DOI: arxiv-2001.01493 Istvan Miklos, Miklos Kresz
Here we prove that counting maximum matchings in planar, bipartite graphs is
#P-complete. This is somewhat surprising in the light that the number of
perfect matchings in planar graphs can be computed in polynomial time. We also
prove that counting non-necessarily perfect matchings in planar graphs is
already #P-complete if the problem is restricted to bipartite graphs. So far
hardness was proved only for general, non-necessarily bipartite graphs.
中文翻译:
计算平面图中的最大匹配很困难
在这里,我们证明计算平面二部图中的最大匹配是#P-complete。鉴于可以在多项式时间内计算平面图中完美匹配的数量,这有点令人惊讶。我们还证明,如果问题仅限于二部图,则计算平面图中不必要的完美匹配已经是#P-complete。到目前为止,仅对一般的、不必要的二部图证明了硬度。
更新日期:2020-01-07
中文翻译:
计算平面图中的最大匹配很困难
在这里,我们证明计算平面二部图中的最大匹配是#P-complete。鉴于可以在多项式时间内计算平面图中完美匹配的数量,这有点令人惊讶。我们还证明,如果问题仅限于二部图,则计算平面图中不必要的完美匹配已经是#P-complete。到目前为止,仅对一般的、不必要的二部图证明了硬度。