Ballots, queues and random graphs
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This paper demonstrates how a simple ballot theorem leads, through the interjection of a queuing process, to the solution of a problem in the theory of random graphs connected with a study of polymers in chemistry. Let Γn(p) denote a random graph with n vertices in which any two vertices, independently of the others, are connected by an edge with probability p where 0 < p < 1. Denote by ρ n(s) the number of vertices in the union of all those components of Γn(p) which contain at least one vertex of a given set of s vertices. This paper is concerned with the determination of the distribution of ρ n(s) and the limit distribution of ρ n(s) as n → ∞and ρ → 0 in such a way that np → a where a is a positive real number.
1989 ◽
Vol 26
(01)
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pp. 103-112
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2014 ◽
Vol 7
(1)
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2018 ◽
Vol 7
(1)
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pp. 77-83
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2014 ◽
Vol 16
(04)
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pp. 1350046
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1964 ◽
Vol 4
(1)
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pp. 122-128
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