Geodesic
On minimal rank over finite fields
The electronic journal of linear algebra, Tome 15 (2006), pp. 210-214.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 05C50, 05C75, 15A03, 15A33
Keywords: minimal rank, forbidden induced subgraph, critical graph 
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Ding, Guoli; Kotlov, Andreĭ. On minimal rank over finite fields. The electronic journal of linear algebra, Tome 15 (2006), pp. 210-214. http://geodesic.mathdoc.fr/item/ELA_2006__15__a12/