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arXiv · 2210.15014

Counting Perfect Matchings in Dense Graphs Is Hard

Nicolas El Maalouly·Yanheng Wang
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Abstract

We show that the problem of counting perfect matchings remains #P-complete even if we restrict the input to very dense graphs, proving the conjecture in [5]. Here "dense graphs" refer to bipartite graphs of bipartite independence number $\leq 2$, or general graphs of independence number $\leq 2$. Our proof is by reduction from counting perfect matchings in bipartite graphs, via elementary linear algebra tricks and graph constructions.

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Nicolas El Maalouly, Yanheng Wang. 2022-10-26. Counting Perfect Matchings in Dense Graphs Is Hard. https://arxiv.org/abs/2210.15014

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