The Dynamic Descriptive Complexity of k-Clique
نویسنده
چکیده
In this work the dynamic descriptive complexity of the kclique query is studied in a framework introduced by Patnaik and Immerman. It is shown that when edges may only be inserted then k-clique can be maintained by a quantifier-free update program of arity k − 1, but it cannot be maintained by a quantifier-free update program of arity k−2 (even in the presence of unary auxiliary functions). This establishes an arity hierarchy for graph queries for quantifier-free update programs under insertions. The proof of the lower bound uses upper and lower bounds for Ramsey numbers.
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