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Given a set $$S$$ S of words, one associates to each word $$w$$ w in $$S$$ S an undirected graph, called its extension graph, and which describes the possible extensions of $$w$$ w in $$S$$ S on the left and on the right. We investigate the family of sets of words defined by the property of the extension graph of each word in the set to be acyclic or connected...
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