Imbalance Conjecture proven and Teschner’s bondage-number conjecture disproven by AI

Hi everyone, I'm a 4th year undergraduate student studying and doing research in theoretical CS. After seeing the recent advancements made by AI in mathematics, especially in graph theory, I bought a ChatGPT Pro subscription to see if AI could solve some graph theory problems I found interesting. After a few days of testing, GPT-5.6 Sol Max was able to solve two open problems in graph theory:

Imbalance conjecture (open for 12+ years) Teschner's bondage-number conjecture (open for 30+ years)

I verified both results independently and asked a friend of mine who specializes in graph theory to check them as well. I submitted both to arXiv, but they removed one after placing a one-submission-per-calendar-month restriction on my new account. I didn't want to wait another month before making this announcement, so I submitted both to another platform. The results are linked below.

A Proof of the Imbalance Conjecture A Counterexample to Teschner's Bondage-Number Conjecture

These are preprints and have not yet undergone peer review.

Also, here are the full chats: Imbalance Conjecture Teschner's Bondage-Number Conjecture