On the structure of Solution-Graphs for Boolean Formulas

@inproceedings{Scharpfenecker2015OnTS,
  title={On the structure of Solution-Graphs for Boolean Formulas},
  author={Patrick Scharpfenecker},
  booktitle={Electronic Colloquium on Computational Complexity},
  year={2015}
}
In this work we extend the study of solution graphs and prove that for boolean formulas in a class called CPSS, all connected components are partial cubes of small dimension, a statement which was proved only for some cases in [16]. In contrast, we show that general Schaefer formulas are powerful enough to encode graphs of exponential isometric dimension and graphs which are not even partial cubes. Our techniques shed light on the detailed structure of st-connectivity for Schaefer and… CONTINUE READING
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