The minimum rank problem over the finite field of order 2: minimum rank 3

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dc.creatorBarrett, Wayne
dc.creatorGrout, Jason
dc.creatorLoewy, Raphael
dc.date2006-12-12
dc.date2008-09-03
dc.date.accessioned2026-07-07T10:00:04Z
dc.date.available2026-07-07T10:00:04Z
dc.descriptionOur main result is a sharp bound for the number of vertices in a minimal forbidden subgraph for the graphs having minimum rank at most 3 over the finite field of order 2. We also list all 62 such minimal forbidden subgraphs. We conclude by exploring how some of these results over the finite field of order 2 extend to arbitrary fields and demonstrate that at least one third of the 62 are minimal forbidden subgraphs over an arbitrary field for the class of graphs having minimum rank at most 3 in that field.
dc.description40 pages, added Sage program and improvements from referee process
dc.identifierhttps://arxiv.org/abs/math/0612331
dc.identifierhttp://arxiv.org/abs/math/0612331
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/168237
dc.subjectCombinatorics
dc.subjectRings and Algebras
dc.subject05C50; 05C75; 15A03
dc.titleThe minimum rank problem over the finite field of order 2: minimum rank 3
dc.typetext

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