In this paper we introduce a new simple strategy into edge-searching of a graph, which is useful to the various subgraph listing problems. Applying the strategy, we obtain the following four algorithms. The first one lists all the triangles in a graph G in O(a(G)m) time, where m is the number of edges of G and a(G) the arboricity of G. The second finds all the quadrangles in O(a(G)m) time. Since a(G) is at most three for a planar graph G, both run in linear time for a planar graph. The third lists all the complete subgraphs K of order in O(la(G)t-2m) time. The fourth lists all the cliques in O(a(G)m) time per clique. All the algorithms require linear space. We also establish an upper bound on a(G) for a graph G: a(G) <-[(2m+ n)1/2/2], where n is the number of vertices in G.

As a method of sharing a secret, e.g., a secret key, Shamir's (k, n) threshold method is well known. However, Shamir's method has a problem in that general access structures cannot be realized. This paper shows that by providing the trustees with several information data concerning the distributed information of the (k, n) threshold method, any access structure can be realized. the update with the change of the secret trustees and the relation to the threshold graph are also discussed.

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