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- W2952586330 abstract "We give upper bounds for the number $Phi_ell(G)$ of matchings of size $ell$ in (i) bipartite graphs $G=(Xcup Y, E)$ with specified degrees $d_x$ ($xin X$), and (ii) general graphs $G=(V,E)$ with all degrees specified. In particular, for $d$-regular, $N$-vertex graphs, our bound is best possible up to an error factor of the form $exp[o_d(1)N]$, where $o_d(1) rightarrow 0$ as $d rightarrow infty$. This represents the best progress to date on the Upper Matching Conjecture of Friedland, Krop, Lundow and Markstrom. Some further possibilities are also suggested." @default.
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- W2952586330 date "2012-05-19" @default.
- W2952586330 modified "2023-09-27" @default.
- W2952586330 title "Asymptotics of the Upper Matching Conjecture" @default.
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