Erdős Problem #601
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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`HasPathOrIndepSetOfType α` holds for an ordinal \(\alpha\) if every simple graph on \(\alpha.\mathrm{ToType}\) contains either: 1. an **infinite path** — an injective function \(f : \mathbb{N} \to \alpha.\mathrm{ToType}\) with \(G.\mathrm{Adj}\, (f n)\, (f(n+1))\) for all \(n\), or 2. an **independent set of order type \(\alpha\)** — a set \(s \subseteq \alpha.\mathrm{ToType}\) that is pairwise non-adjacent in \(G\) and whose order type (under the well-order inherited from \(\alpha\)) equals \(\alpha\).
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Every rayless instance reduces rigorously to a full-type finite-kernel column graph with a ccc finite-independent-set poset; the remaining CH-frontier obstruction is the full-order kernel avoidance pl
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