Erdos's Question on the Independence Ratio of Unit-Distance Graphs
Erdos asked whether a finite unit-distance graph in the plane can have independence ratio below $1/4$. One exists, built on the geometric fractional chromatic number framework of Matolcsi, Ruzsa, Varga and Zsamboki plus a carefully chosen two-vertex augmentation.
Exact FrontierDelta
Scope and record
Occurred: Jun 26, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-assisted. Imported under CC BY 4.0.
Canonical aliases: Erdos's Question on the Independence Ratio of Unit-Distance Graphs · Unit-distance independence
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Akos Ducz
human · human collaborator
Daniel Varga
human · human collaborator
ChatGPT
model · ai model contributor · OpenAI
Codex (GPT-5.5)
model · ai model contributor · OpenAI
Lineage and corrections
This event attributed to Akos Ducz
This event attributed to Daniel Varga
This event attributed to ChatGPT
This event attributed to Codex (GPT-5.5)