Thin Tree Verification is coNP-Complete
Published:Dec 31, 2025 18:38
•1 min read
•ArXiv
Analysis
This paper addresses the computational complexity of verifying the 'thinness' of a spanning tree in a graph. The Thin Tree Conjecture is a significant open problem in graph theory, and the ability to efficiently construct thin trees has implications for approximation algorithms for problems like the asymmetric traveling salesman problem (ATSP). The paper's key contribution is proving that verifying the thinness of a tree is coNP-hard, meaning it's likely computationally difficult to determine if a given tree meets the thinness criteria. This result has implications for the development of algorithms related to the Thin Tree Conjecture and related optimization problems.
Key Takeaways
- •Proves that verifying the thinness of a tree is coNP-hard.
- •This result has implications for the computational complexity of problems related to the Thin Tree Conjecture.
- •The findings impact the development of algorithms for related optimization problems, such as the ATSP.
Reference
“The paper proves that determining the thinness of a tree is coNP-hard.”