Orthogonal Representations, Projective Rank, and Fractional Minimum Positive Semidefinite Rank: Connections and New Directions

• Main Authors: Hogben, Leslie, Palmowski, Kevin F, Roberson, David E, Severini, Simone
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2017
• Subjects: Orthogonal representation; Projective rank
• Online Access: https://hdl.handle.net/10356/83454; http://hdl.handle.net/10220/43551
• Institution: Nanyang Technological University

Fractional minimum positive semidefinite rank is defined from r-fold faithful orthogonal representations and it is shown that the projective rank of any graph equals the fractional minimum positive semidefinite rank of its complement. An r-fold version of the traditional definition of minimum positi...