Abstract
We study the class of all finite directed graphs (digraphs) up to primitive positive constructibility. The resulting order has a unique maximal element, namely the digraph P1 with one vertex and no edges. The digraph P1 has a unique maximal lower bound, namely the digraph P2 with two vertices and one directed edge. Our main result is a complete description of the maximal lower bounds of P2; we call these digraphs submaximal. We show that every digraph that is not equivalent to P1 and P2 is below one of the submaximal digraphs.
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The authors would like to thank the anonymous referees for thoroughly reading our article as well as giving helpful comments that improved the final article.
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The second author is supported by DFG Graduiertenkolleg 1763 (QuantLA).
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Bodirsky, M., Starke, F. Maximal Digraphs with Respect to Primitive Positive Constructability. Combinatorica 42 (Suppl 1), 997–1010 (2022). https://doi.org/10.1007/s00493-022-4918-1
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DOI: https://doi.org/10.1007/s00493-022-4918-1