Sivaraman's Perfect-Divisibility Characterization Question
Sivaraman asked whether perfect divisibility is characterized by its chromatic consequence: is a graph $G$ perfectly divisible if and only if $\chi(H) \le \binom{\omega(H)+1}{2}$ for every induced subgraph $H$ of $G$? False: the Paley graph $P(17)$ satisfies the chromatic bound hereditarily but is not perfectly divisible.
Exact FrontierDelta
Scope and record
Occurred: Aug 14, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: preprint. AI contribution: ai-co-developed. Imported under CC BY 4.0.
Canonical aliases: Sivaraman's Perfect-Divisibility Characterization Question · Perfect divisibility vs chi-bound
Confidence: Not scored
Registry verification: unreviewed · preprint · resolved
Attribution
VibeMathed
registry · event recorded by
Zhiyu Wang
human · human collaborator
Weihao Xia
human · human collaborator
ChatGPT
model · ai model contributor · OpenAI
Lineage and corrections
This event attributed to Weihao Xia
This event attributed to Zhiyu Wang
This event attributed to ChatGPT