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Number of Variables for Graph Identification and the Resolution of GI Formulas
[article]
2021
Electronic colloquium on computational complexity
We show that the number of variables and the quantifier depth needed to distinguish a pair of graphs by first-order logic sentences exactly match the complexity measures of clause width and positive depth needed to refute the corresponding graph isomorphism formula in propositional narrow resolution. Using this connection, we obtain upper and lower bounds for refuting graph isomorphism formulas in (normal) resolution. In particular, we show that if k is the minimum number of variables needed to
dblp:journals/eccc/ToranW21
fatcat:572wgmfwnngojjrmpypomagari