A hierarchy of randomness for graphs Original Research Article

In this paper we formulate four families of problems with which we aim at distinguishing different levels of randomness. The first one is completely non-random, being the ordinary Ramsey–Turán problem and in the subsequent three problems we formulate some randomized variations of it. As we will show, these four levels form a hierarchy. In a continuation of this paper we shall prove some further theorems and discuss some further, related problems.