Evasiveness and Closure Operators

One of the classical applications of topological methods in combinatorics is the proof of the so-called Evasiveness Conjecture for graphs whose number of vertices is a prime power. In this chapter we describe the framework of the problem, sketch the original argument, and prove some important facts about nonevasiveness. One of the important tools is the so-called closure operators, which are also useful in other contexts. 

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