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The minimum rank problem over the finite field of order 2: Minimum rank 3 |
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| Authors: | Wayne Barrett Raphael Loewy |
| Institution: | a Department of Mathematics, Brigham Young University, Provo, UT 84602, USA b Department of Mathematics, Iowa State University, Ames, IA 50011, USA c Department of Mathematics, Technion-Israel Institute of Technology, Haifa 32000, Israel |
| Abstract: | Our 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. |
| Keywords: | Primary: 05C50 Secondary: 05C75 15A03 |
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