Avoidability of circular formulas
Discrete Mathematics
2016-10-17 v1
Abstract
Clark has defined the notion of -avoidance basis which contains the avoidable formulas with at most variables that are closest to be unavoidable in some sense. The family of circular formulas is such that , , and so on. For every , the -avoidance basis contains . Clark showed that the avoidability index of every circular formula and of every formula in the -avoidance basis (and thus of every avoidable formula containing at most 3 variables) is at most 4. We determine exactly the avoidability index of these formulas.
Cite
@article{arxiv.1610.04439,
title = {Avoidability of circular formulas},
author = {Guilhem Gamard and Pascal Ochem and Gwenaël Richomme and Patrice Séébold},
journal= {arXiv preprint arXiv:1610.04439},
year = {2016}
}