The Depth First Search (DF.S.) algori.thm i§. one of the basic techniques which is used in a very large variety of graph algorithms. Every -application' of the DFS involves, beside traversing the graph, cOnstructing a special structured tree, called a DFS tree. In this paper, we give a complete characterization of all the graphs in which every spanning tree is ~ 'DFS tree. These graphs are call...

Dual EC is an algorithm to compute pseudorandom numbers starting from some random input. Dual EC was standardized by NIST, ANSI, and ISO among other algorithms to generate pseudorandom numbers. For a long time this algorithm was considered suspicious – the entity designing the algorithm could have easily chosen the parameters in such a way that it can predict all outputs – and on top of that it...

Let X = S " ' x . . . x S"" be a product of spheres of total dimension n=nl+n2 +... +nk. A fundamental unanswered question is the determination of which finite groups can act freely on X and what actions on the cohomology so arise. In particular it is conjectured that if an elementary abelian group acts freely, then its rank is less than or equal to k. Great progress has been made recently on t...