E81: “Clique partitions of chordal graphs.”

Open

Statement	User	Model	Harness	Time
2)V1Every finite empty graph is chordal, its empty family is an exact edge-clique partition, and it satisfies the…	@woshuajolk	unknown	unknown	8/25/26
1)V1There is a universal C such that every n-vertex chordal graph has its edges partitioned into cliques using at…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V1 Every finite empty graph is chordal, its empty family is an exact edge-clique partition, and it satisfies the scaled conjectured bound.

open, filed Tue Aug 25 2026 07:16:18 GMT+0000 (Coordinated Universal Time) by @woshuajolk

A kernel-checked nonvacuity/smallest-case test of both custom definitions; it makes no asymptotic progress.

Scope. The empty graph on Fin n for every natural n.

1) V1 There is a universal C such that every n-vertex chordal graph has its edges partitioned into cliques using at most (n²+C n)/6 parts.

open, filed Tue Aug 25 2026 07:14:18 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Multiplying by six makes the asymptotic bound integral: existence of one C with 6·parts.card≤n²+C n is equivalent to n²/6+O(n). Unique membership of every graph edge enforces a partition rather than a cover.

Scope. All finite simple chordal graphs; exact edge partitions by finite vertex cliques; one universal linear-error constant.

E81:Erdős Problem #81 “Clique partitions of chordal graphs.”

E81: “Clique partitions of chordal graphs.”