Mapping in random-structures

A mapping in random-structures is defined on the vertices of a generalized hypercube Q{sub {alpha}}{sup n}. A random-structure will consist of (1) a random contact graph and (2) a family of relations imposed on adjacent vertices. The vertex set of a random contact graph will be the set of all coordinates of a vertex P {element_of} Q{sub {alpha}}{sup n}. Its edge will be the union of the edge sets of two random graphs. The first is a random 1-regular graph on 2m vertices (coordinates) and the second is a random graph G{sub p} with p = c{sub 2}/n on all n vertices (coordinates). The structure of the random contact graphs will be investigated and it will be shown that for certain values of m, c{sub 2} the mapping in random-structures allows to search by the set of random-structures. This is applied to mappings in RNA-secondary structures. Also, the results on random-structures might be helpful for designing 3D-folding algorithms for RNA