A topological approach to evasiveness

Jeff Kahn, Michael Saks, Dean Sturtevant
1984 Combinatorica  
The complexity of a digraph property is the number of entries of the vertex adjacency matrix of a digraph which must be examined in worst case to determine whether the graph has the property. Rivest and Vuillemin proved the result (conjectured by Aanderaa and Rosenberg) that every graph property that is monotone (preserved by addition of edges) and nontrivial (holds for some but not all graphs) has complexity £2(v ~) where v is the number of vertices. Karp conjectured that every such property
more » ... evasive, i.e., requires that every entry of the incidence matrix be examined. In this paper the truth of Karp's conjecture is shown to follow from another conjecture concerning group actions on topological spaces. A special case of the conjecture is proved which is applied to prove Karp's conjecture for the case of properties of graphs on a prime power number of vertices.
doi:10.1007/bf02579140 fatcat:wmx24dtqjvfg7g5amsijweow64