{"id":"palomar/PALOMAR-2026-09-30-000001","url":"https://github.com/mmislan/palomar-p029-digraph-support-families/tree/579ba54f592330e8fd972d9e5af02699f7fead6c","json":"https://data.palomar-registry.org/entries/PALOMAR-2026-09-30-000001-v1.json","repo":"https://github.com/mmislan/palomar-p029-digraph-support-families","tags":["math.CO","msc:05C20","msc:06A15","msc:05D05","combinatorics","digraphs","autocatalytic-networks","set-systems"],"score":0,"title":"Characterizing digraph support families by rooted-interval deletion","trust":"high","domain":"math.CO","source":"palomar","authors":["Michael Mislan"],"reviews":0,"subject":"math.CO","summary":"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…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"verified":true,"discussed":0,"published":"2026-09-30","reactions":{},"formalized":true,"formalizes":[{"title":"An intrinsic interval-deletion characterization of digraph support families","identifier":"","relationship":"formalizes"}]}