The minimum rank problem: A counterexample
โ Scribed by Swastik Kopparty; K.P.S. Bhaskara Rao
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 100 KB
- Volume
- 428
- Category
- Article
- ISSN
- 0024-3795
No coin nor oath required. For personal study only.
๐ SIMILAR VOLUMES
It has been conjectured by C. van Nuffelen that the chromatic number of any graph with at least one edge does not exceed the rank of its adjacency matrix. We give a counterexample, with chromatic number 32 and with an adjacency matrix of rank 29.
The minimum rank of a graph is the smallest possible rank among all real symmetric matrices with the given graph. The minimum semidefinite rank of a graph is the minimum rank among Hermitian positive semidefinite matrices with the given graph. We explore connections between OS-sets and a lower bound