An optimal lower bound on the number of variables for graph identifications

@article{Cai1992AnOL,
  title={An optimal lower bound on the number of variables for graph identifications},
  author={Jin-Yi Cai and Martin F{\"u}rer and Neil Immerman},
  journal={Combinatorica},
  year={1992},
  volume={12},
  pages={389-410}
}
In this paper we show that (n) variables are needed for rst-order logic with counting to identify graphs on n vertices. The k-variable language with counting is equivalent to the (k ? 1)-dimensional Weisfeiler-Lehman method. We thus settle a long-standing open problem. Previously it was an open question whether or not 4 variables suuce. Our lower bound remains true over a set of graphs of color class size 4. This contrasts sharply with the fact that 3 variables suuce to identify all graphs of… CONTINUE READING
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