Uncountably Many Minimal Hereditary Classes of Graphs of Unbounded Clique-Width

@article{Brignall2022UncountablyMM,
  title={Uncountably Many Minimal Hereditary Classes of Graphs of Unbounded Clique-Width},
  author={Robert Brignall and Daniel G. Cocks},
  journal={Electron. J. Comb.},
  year={2022},
  volume={29}
}
Given an infinite word over the alphabet $\{0,1,2,3\}$, we define a class of bipartite hereditary graphs $\mathcal{G}^\alpha$, and show that $\mathcal{G}^\alpha$ has unbounded clique-width unless $\alpha$ contains at most finitely many non-zero letters. We also show that $\mathcal{G}^\alpha$ is minimal of unbounded clique-width if and only if $\alpha$ belongs to a precisely defined collection of words $\Gamma$. The set $\Gamma$ includes all almost periodic words containing at least one non… 

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