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Claim. Lezhe Gao's manuscript Peeling Hypergraphs: A Structural Sufficient Condition for Property B, a Zenodo deposit of 22 July 2026 filed on the proof-claims tab of Problem 602 on 1 October 2026, calls a finite hypergraph peeling if its edges can be ordered so that each edge brings at least two vertices not in any earlier edge, or one such vertex together with a vertex of an earlier edge. It proves that every peeling hypergraph has Property B and characterizes peeling hypergraphs by acyclic assignments of vertices to edges; for graphs the peeling ones are exactly the forests.
Submission note. Posted to erdosproblems.com as a proof claim by Lezhe Gao (account lezhe) on 1 October 2026, giving "DeepSeek & GPT-5.5" as the AI used:
This paper introduces peeling hypergraphs, a structural sufficient condition for Property B. A hypergraph is peeling if its edges can be ordered so that each edge introduces at least two new vertices, or one new vertex while also touching earlier ones. The main theorem gives an equivalent characterization via acyclic vertex-to-edge assignments. Peeling is shown to generalize forests for graphs, with cycles as minimal obstructions. The paper does not resolve Erdős Problem #602, as it focuses on finite hypergraphs; it is a partial result offering a new combinatorial criterion for Property B. Notes: This paper exclusively studies finite hypergraphs. It does not address the infinite almost-disjoint family setting of Erdős Problem #602. No compactness argument, transfinite construction, or reduction from the infinite case to the finite case is provided. Therefore, this submission is not a proof of, nor a genuine partial solution to, the original infinite problem. It is submitted solely as a related finite structural criterion for Property B, in case it stimulates further work on the infinite version.
Why it is rejected. It does not address the Statement.
Problem 602 asks whether every family of
countably infinite sets, any two meeting in a finite set of size other than
, has a -coloring of its union with no set monochromatic. The claim
addresses instead a criterion for Property B of finite hypergraphs, and, as
its author says, gives no compactness argument, transfinite construction or
reduction from the infinite case, so its mathematics settles no instance of
this problem. The value proved is its answer to that criterion.
Standing. Rejected, as not addressing the Statement. The entry carries no comments and no review, and this corpus has not checked the manuscript.
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