In this Master thesis, we will propose a way to solve k-set agreement in a very relaxed model of a synchronous distributed system. The model is based on a sequence of directed communication graphs determined by the adversary, which specify which process receives a message from which process in a round. k-set agreement describes the problem where distributed process with possible different initial values have to agree on a smaller set of decision values. In order to make k-set agreement solvable, the power of the adversary w.r.t. disrupting communication between processes must be restricted. Essentially, the proposed restrictions ensure that, during every execution, certain strongly connected subgraphs (vertex stable root components) are influencing each other and that, eventually, communication graphs are sufficiently stable for a short time to ensure termination. We will show that an algorithm exists, which can solve k-set agreement under these weak constraints, and prove its correctness. Basically, the algorithm locally estimates whether a vertex stable root component has formed and, if so, tries to use its strong connectivity to force all its members to decide on the same value. The algorithm is k-uniform, i.e., independent of k, hence automatically adapts the number of different decision values according to the actual network conditions. The result of this work, which has been supported by Austrian Science Fund (FWF) project RiSE (S11405), have been published at the 17th International Conference on the Principles of Distributed Systems (OPODIS 2013).