Claims

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2026_06_17_agbanwa: A Zenodo note proves cp(G) at most (2n-1)²/24 + 2 for every chordal graph on n vertices having a maximum clique whose edge deletion lowers the clique number by at most one, excluding the extremal split graphs; unreviewed.

2026_08_23_traverso: Paper III of Traverso's series asserts that every split graph on n vertices has a clique partition into n²/6 + O(n) cliques, the sharp coefficient, with a Lean 4 freeze the author reports as unconditional; the split case only.

2026_09_08_morluto_luo_huang_lee: A manuscript and Lean 4 development in the N0zoM1z0/erdos-81 repository assert that for all large n the maximum clique partition number of a chordal graph is floor(n(n+1)/6), so n²/6 + O(n); the Lean assumes three theorems.

2026_09_15_okechukwu: An arXiv preprint determines the eventual maximum clique partition number of graphs with rooted simplicial defect s; the case s = 0 is the chordal graphs, giving cp(G) at most n²/6 + n/6 + O(1); announced on the thread; unreviewed.

2026_09_22_traverso: Paper IV of Traverso's series asserts that every chordal graph on n vertices has a partition into at most floor(n(n+1)/6) + b cliques of order at most four, hence n²/6 + O(n), with a Lean 4 proof the author reports unconditional.

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