Catherine S. Greenhill, M. Isaev, Tamás Makai, B. McKay
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引用次数: 0
Abstract
We find an asymptotic enumeration formula for the number of simple
$r$
-uniform hypergraphs with a given degree sequence, when the number of edges is sufficiently large. The formula is given in terms of the solution of a system of equations. We give sufficient conditions on the degree sequence which guarantee existence of a solution to this system. Furthermore, we solve the system and give an explicit asymptotic formula when the degree sequence is close to regular. This allows us to establish several properties of the degree sequence of a random
$r$
-uniform hypergraph with a given number of edges. More specifically, we compare the degree sequence of a random
$r$
-uniform hypergraph with a given number edges to certain models involving sequences of binomial or hypergeometric random variables conditioned on their sum.
期刊介绍:
Published bimonthly, Combinatorics, Probability & Computing is devoted to the three areas of combinatorics, probability theory and theoretical computer science. Topics covered include classical and algebraic graph theory, extremal set theory, matroid theory, probabilistic methods and random combinatorial structures; combinatorial probability and limit theorems for random combinatorial structures; the theory of algorithms (including complexity theory), randomised algorithms, probabilistic analysis of algorithms, computational learning theory and optimisation.