The maximum corank of graphs with a 2-separation |
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Authors: | Hein van der Holst |
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Institution: | Department of Mathematics and Computer Science, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands |
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Abstract: | For a graph G=(V,E) with vertex-set V={1,2,…,n}, which is allowed to have parallel edges, and for a field F, let S(G;F) be the set of all F-valued symmetric n×n matrices A which represent G. The maximum corank of a graph G is the maximum possible corank over all A∈S(G;F). If (G1,G2) is a (?2)-separation, we give a formula which relates the maximum corank of G to the maximum corank of some small variations of G1 and G2. |
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Keywords: | 05C50 15A18 |
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