Annals of Combinatorics 4 (2000) 375-382


Random Structures

Christian M. Reidys

Los Alamos National Laboratory, TSA 2, NM 87545, USA
duck@tsasa.lanl.gov

Received September 14, 1998

AMS Subject Classification: 05C38, 05C40, 05C80, 05C90

Abstract. A random structure, sn, consists of (i) a random contact graph X with vertex set {1,..., n} and (ii) a multi-set of binary relations over the finite set $ {\cal A}$, associated with the edges of X. The X-edges are the union of the edge sets of two random graphs, X1 and X2. X1 is a random partial one factor graph over the vertices$ \{\ell_{i_1},\dots,\ell_{i_{2m}}\}$ and has edge set {y1, ...,ym}. X2 has vertex set {1, ...,n} and is obtained by selecting the edges of Kn \ {y1,...,ym} with independent probability p={c2 / n},c2>0. This paper provides a probabilistic analysis of the contact graphs of random structures and puts the results into context with the evolutionary optimization of biopolymers.

Keywords: random structure, random graph, connectivity, branching process


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