Breakthrough Tracker record
An AI-generated graph is claimed to disprove Teschner's bondage-number conjecture
Yousof Yavari gives a connected 18-vertex cubic bipartite graph with domination number six and bondage number five, contradicting Teschner's proposed bound b(G) ≤ 3Δ(G)/2.
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- Stable ID
math-teschner-bondage-number-counterexample-2026- Revision
math-teschner-bondage-number-counterexample-2026.v1- Field
- Mathematics · Graph theory, domination and exact finite verification
- Evidence
- Tier 1 · Peer reviewed: No
- Record state
- Provisional · Provisional computer-certified counterexample
- Last checked
AI role
The author states that GPT-5.6 Sol Max generated the counterexample after being prompted to solve the problem. Yavari revised and expanded the proof and accepts responsibility; Eric Hou is thanked for independent verification.
Record details
- Problem or result
- Teschner's upper-bound conjecture for graph bondage numbers
- Authors
- Yousof Yavari
- Institutions
- University of British Columbia
- Result date
- Preprint submitted September 1 and announced September 7, 2026
Why it matters
A small explicit graph would settle a three-decade-old universal bound negatively, and the complete standard-library verifier makes every finite enumeration independently reproducible.
Limits
The nine-page manuscript is not peer reviewed. The exact verifier checks the stated graph and all four-edge deletion sets, but the tracker did not independently rerun it in this cycle.
Sources
Correction and revision history
- 2026-09-07 — Added after primary-source, scope, status, AI-role and limitation review.
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