{"id":"hexagon/2610.00391","pdf":"https://hexagonmath.org/pdf/2610.00391v1","url":"https://hexagonmath.org/abs/2610.00391v1","tags":["cs.LO","msc:05C20","msc:06A15","msc:05D05","Lean formalization","RAF realizability","digraph support families","interior operators","rooted-interval deletion","single-head Horn theories"],"score":0,"title":"An intrinsic interval-deletion characterization of digraph support families","domain":"math.CO","origin":"ai-generated","source":"hexagon","authors":["Michael Mislan"],"reviews":0,"subject":"math.CO","summary":"For a finite directed graph with loops allowed, its supported subsets are those in which every vertex has an in-neighbour within the subset. We characterize exactly which set families arise this way on their original ground set. Starting from the power set, a legal step chooses an inclusion-maximal remaining nonmember, selects a previously unused root absent from every target-family member below it, and deletes the rooted interval. A family is a digraph support family if and only if some legal deletion sequence reaches it. The maximal residual set may follow any fixed valid policy; only…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-20","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":true,"formalizations":["https://palomar-registry.org/entry?id=PALOMAR-2026-09-30-000001&version=1"],"human_understanding":"some"}