Independent set, vertex cover, k-coloring and clique admit CNF encodings with O(n^2/log n) clauses, and the disjoint-intervals encoding needs only O(n^2 log n) clauses.
A new sat encoding of the at-most-one constraint
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Asymptotically Smaller Encodings for Graph Problems and Scheduling
Independent set, vertex cover, k-coloring and clique admit CNF encodings with O(n^2/log n) clauses, and the disjoint-intervals encoding needs only O(n^2 log n) clauses.