Characterizing digraph support families by rooted-interval deletion
We answer the set-theoretic characterization question for digraph support families posed by Mike Steel in Section 4 of Interior operators and their relationship to autocatalytic networks (arXiv:2305.16714v4, 2023). A digraph on a finite set E is given by a predecessor map P assigning to each vertex e a set P(e) of in-neighbours, loops allowed, and a set S is supported when every element e of S has some element of S in P(e). The characterization refers only to the family F. Start from the full power set of E with no roots used. A legal step chooses a remaining set S outside F that is…
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