The relationship between triangle size and minimum rank for 7 × 7 zero-nonzero patterns

Abstract

In this paper, a positive answer to the question (I) in Johnson and Link [C. R. Johnson, J. A. Link, The extent to which triangular sub-patterns explain minimum rank, Discrete Applied Mathematics, 156 (2008) 1637-1651] is given for 7 × 7 zero-nonzero patterns.

Subject Classification: (2010):

• 05C50
• 15B35
• 05C05
• 15A03
• 15A18

Keywords:

• Minimum rank
• Asymmetric zero-nonzero pattern
• Triangle pattern