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arXiv · 1610.09089

The Dynamic Descriptive Complexity of k-Clique

Thomas Zeume
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Abstract

In this work the dynamic descriptive complexity of the k-clique query is studied. 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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Thomas Zeume. 2016-10-28. The Dynamic Descriptive Complexity of k-Clique. https://arxiv.org/abs/1610.09089

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