A similarity relation is a relation on words of equal length induced by a symmetric and reflexive relation on letters. The aim of this article is to give an overview of the results concerning repetition-freeness in connection with similarity relations. We consider so called chain relations, cyclic relations and partial words, which can be seen as a special case of similarity relations. As a new result, we prove that local 3~+-repetitions can be avoided in binary partial words and the local avoidability index of R-cubes is five, where R is a relation such that the graph of the relation is a cycle.
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