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IMADA -Department of Mathematics and Computer Science |
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In the 1960s, statistical physicists discovered a fascinating algorithm for counting perfect matchings in planar graphs. Valiant later showed that the same problem is #P-hard for general graphs. Since then, the algorithm for planar graphs was extended to bounded-genus graphs, to graphs excluding $K_{3,3}$ or $K_5$ as a minor, and more generally, to any graph class excluding a fixed minor H that can be drawn in the plane with a single crossing. This stirred up hopes that counting perfect matchings might be polynomial-time solvable for graph classes excluding any fixed minor H. Alas, in this paper, we show #P-hardness for $K_8$-minor-free graphs by a simple and self-contained argument. Joint work with Mingji Xia, Chinese Academy of Sciences, China Host: Rolf Fagerberg SDU HOME | IMADA HOME Daniel Merkle |