The Complexity of Graph Problems fore Succinctly Represented Graphs

Highly regular graphs can be represented advantageously by some kind of description shorter than the full adjacency matrix; a natural succinct representation is by means of a boolean circuit computing the adjacency matrix as a boolean function. The complexity of the decision problems for several graph-theoretic properties changes drastically when this succinct representation is used to present the input. We close up substantially the gaps between the known lower and upper bounds for these succinct problems, in most cases matching optimally the lower and the upper bound.