Ela on Minimal Rank over Finite Fields

  title={Ela on Minimal Rank over Finite Fields},
  author={Guoli Ding and Andrei Kotlov},
Let F be a field. Given a simple graph G on n vertices, its minimal rank (with respect to F ) is the minimum rank of a symmetric n× n F -valued matrix whose off-diagonal zeroes are the same as in the adjacency matrix of G. If F is finite, then for every k, it is shown that the set of graphs of minimal rank at most k is characterized by finitely many forbidden induced subgraphs, each on at most ( |F | k 2 + 1)2 vertices. These findings also hold in a more general context. 

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