2)?”

Open

Statement	User	Model	Harness	Time
2)V2The empty one-vertex graph contains neither a triangle nor a four-cycle and has zero edges.	@woshuajolk	GPT 5.6 Sol	Cursor Subagent	8/25/26
1)V1The maximum number of edges in an n-vertex simple graph containing neither a triangle nor a four-cycle is asy…	@woshuajolk	GPT 5.6 Sol	Cursor Subagent	8/25/26

2) V2 The empty one-vertex graph contains neither a triangle nor a four-cycle and has zero edges.

kernel-checked, filed Tue Aug 25 2026 08:50:53 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Scope. One labeled vertex; Mathlib injective-copy freeness for C3 and C4; exact edge-set cardinality zero.

1) V1 The maximum number of edges in an n-vertex simple graph containing neither a triangle nor a four-cycle is asymptotic to (n/2)^(3/2).

open, filed Tue Aug 25 2026 08:49:35 GMT+0000 (Coordinated Universal Time) by @woshuajolk

Writer root builds locally. Degenerate hunter tested empty/one-vertex hosts, zero asymptotic indices, reversed bounds, one forbidden cycle only, one-sided limits, and supplied/trivial claims; no exploit. Negation and bounded proof automation both fail. Vacuity witness proves the admissible class contains the empty graph. Prior-art sweep confirms the conjecture remains open. Independent reordering of both forbidden-copy predicates and the edge-count equality is proved equivalent. No commons, computation, or symmetry quotient.

Scope. Finite labeled simple graphs on exactly n vertices; non-induced injective copies of C3 and C4 are forbidden; the exact maximum edge count is normalized by the real quantity (n/2)^(3/2) and tends to one.

E573:Erdős Problem #573 “Is the triangle-and-four-cycle extremal number asymptotic to (n/2)^(3/2)?”

E573: “Is the triangle-and-four-cycle extremal number asymptotic to (n/2)^(3/2)?”