Publication v7
Sharp special cases, the directed triangle question and the stronger rainbow formulation.
Formal proofs: No exact, source-pinned formal proof of the full conjecture was identified in this source selection. No OpenMath formalization task or execution is attached.
AI-assisted work: The selected papers do not report AI assistance; companion computer arithmetic is described separately.
Sullivan’s 2006 survey; Hladký–Král’–Norin v4 and its 2017 publication; Hompe–Huynh v4 and its 2025 publication. This is a scoped selection checked on 12 October 2026, not an exhaustive search.
Checked Oct 12, 2026 · independent review pending.
Conjecture 2.1; no current-status report · observed Oct 1, 2026 · superseded
Source status dated Apr 14, 2006 · observed Oct 1, 2026
The cited source item and version only; this is not an independent OpenMath assessment.
Open question in cited source · observed Oct 12, 2026
Source status date unavailable · observed Oct 12, 2026
The published 2025 paper presents the full directed cycle bound as an open conjecture; partial results below retain their own assumptions.
Blair D. Sullivan; hosted by American Institute of Mathematics · metadata-link · Not established; links and OpenMath paraphrases only
Store metadata and original OpenMath paraphrases; follow the original source for authoritative wording. Rights / source terms
caccetta-haggkvist:entry:0:v1caccetta-haggkvist:entry:small-degree:v1caccetta-haggkvist:entry:transitive:v1caccetta-haggkvist:entry:large-order:v1Jan Hladký; Daniel Král’; Sergey Norin · metadata-link · Metadata, links and original OpenMath paraphrases only
Follow the original source for authoritative statements and reuse terms. Rights / source terms
caccetta-haggkvist:entry:triangle-bound:v1caccetta-haggkvist:entry:triangle-target:v1Patrick Hompe; Tony Huynh · metadata-link · Metadata, links and original OpenMath paraphrases only
Follow the original source for authoritative statements and reuse terms. Rights / source terms
caccetta-haggkvist:entry:rainbow:v1caccetta-haggkvist:entry:rainbow-additive:v1Initial checked pilot publication; source attribution, rights, wording and coverage reviewed by OpenMath staff.
Add cited resolution scope and consolidate equivalent prime formulations and supporting Claims; mathematical evidence and execution review remain distinct.
Publish checked pilot curation with canonical Claims and scoped progress; preserve exact source revisions, assumptions, coverage limits and historical publications. External artifacts and OpenMath execution remain distinct.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.
Reviewed reader correction: preserve assertion history, exact citations and scoped assessments; task evidence names its exact Claim target.