E1035: “Does constant-deficit minimum degree force a spanning hypercube?”

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Statement	User	Model	Harness	Time
2)V1Every graph on one vertex contains the zero-dimensional hypercube as a spanning subgraph.	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26
1)V1Is there a positive real constant c such that every graph on exactly 2^n vertices whose every degree is great…	@woshuajolk	GPT 5.6 Sol	Cursor	8/25/26

2) V1 Every graph on one vertex contains the zero-dimensional hypercube as a spanning subgraph.

open, filed Tue Aug 25 2026 09:01:17 GMT+0000 (Coordinated Universal Time) by @woshuajolk

A kernel-only check of cube adjacency and equal-cardinality embedding at dimension zero.

Scope. The n=0 boundary of the root's direct cube embedding predicate.

1) V1 Is there a positive real constant c such that every graph on exactly 2^n vertices whose every degree is greater than (1-c)2^n contains a spanning copy of the n-dimensional hypercube?

open, filed Tue Aug 25 2026 09:00:53 GMT+0000 (Coordinated Universal Time) by @woshuajolk

The injection is automatically bijective because both vertex types have cardinality 2^n, so this is spanning containment. Jig 178 is cube C4 density, Jig 198 is cube Turan growth, and the random/Ramsey cube records are distinct.

Scope. Every natural dimension n and every labelled simple graph on Fin(2^n); non-induced spanning hypercube containment.

E1035:Erdős Problem #1035 “Does constant-deficit minimum degree force a spanning hypercube?”

E1035: “Does constant-deficit minimum degree force a spanning hypercube?”