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Claim. For a fixed integer $s\ge0$, consider the graphs in which every induced subgraph has, outside every prescribed clique, a vertex whose neighborhood becomes a clique after deleting at most $s$ vertices; the graphs with $s=0$ are exactly the chordal graphs. Obinna Okechukwu, Clique partitions and bounded simplicial defect, arXiv:2609.20871 (24 pages, math.CO, posted 15 September 2026, the claim's date), asserts that for each fixed $s$ the largest clique partition number at every sufficiently large order $n$ is $\lfloor(n+s)(n+s+1)/6\rfloor-\binom{s+1}2$, determines all graphs attaining it, and shows that the same expression bounds the clique partition number up to an additive constant depending only on $s$ at every order. For $s=0$ this gives, as the abstract states, that every chordal graph has clique partition number at most $n^2/6+n/6+O(1)$, answering the question of Erdős, Ordman and Zalcstein that is Problem 81 with yes. The abstract describes the method as signed fractional localization combined with an edge-disjoint triangle construction, needing only a qualitative fractional-packing approximation, and adds structural stability for sublinear defect and a finite-order theorem for integer signed clique functionals. This record rests on the arXiv abstract (as of 2026-10-07); this corpus has not checked the paper's proofs. Traverso's Paper IV cites the paper's Corollary 1.2 as obtaining the additive bound and eventual maximum for chordal graphs as a special case and its Theorem 1.1 for the extremal family.

Depends on. Nothing in this wiki.

Standing. Claimed: an arXiv preprint with no refereed version, no formalization and no outside review known to this corpus. The author announced it in a comment of 21 September 2026 on the site's claim of Morluto, Luo, Huang and Lee, whose manuscript the tab credits to GPT-5.6 and GPT-6 Astra, stating that the author had solved the problem earlier in the month by a different and more general approach; the submitters of that claim replied that the arXiv posting followed their public release by a week and asked for a disclosure of AI use, which the abstract does not carry. The priority dispute is recorded, not adjudicated. The paper is not registered on the site's proof-claims tab, and the site labels the problem OPEN (page last edited 28 December 2025, as of 2026-10-07).