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• W2949152304 abstract "Let J and J* be subsets of Z+ such that 0,1in J and 0in J*. For infinitely many n, let k=(k_1,..., k_n) be a vector of nonnegative integers whose sum M is even. We find an asymptotic expression for the number of multigraphs on the vertex set {1,..., n} with degree sequence given by k, such that every loop has multiplicity in J* and every non-loop edge has multiplicity in J. Equivalently, these are symmetric integer matrices with values J* allowed on the diagonal and J off the diagonal. Our expression holds when the maximum degree K satisfies K = o(M^(1/3)). We prove this result using the switching method, building on an asymptotic enumeration of simple graphs with given degrees (McKay and Wormald, 1991). Our application of the switching method introduces a novel way of combining several different switching operations into a single computation." @default.
• W2949152304 created "2019-06-27" @default.
• W2949152304 creator A5014961672 @default.
• W2949152304 creator A5031194096 @default.
• W2949152304 date "2013-03-18" @default.
• W2949152304 modified "2023-09-27" @default.
• W2949152304 title "Asymptotic enumeration of sparse multigraphs with given degrees" @default.
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• W2949152304 hasPublicationYear "2013" @default.
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