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http://hdl.handle.net/1942/15199
Title: | Nullity and loop complementation for delta-matroids | Authors: | BRIJDER, Robert Hoogeboom, Hendrik Jan |
Issue Date: | 2013 | Publisher: | SIAM PUBLICATIONS | Source: | SIAM JOURNAL ON DISCRETE MATHEMATICS, 27 (1), p. 492-506 | Abstract: | We show that the symmetric-difference distance measure for set systems, and more specifically for delta-matroids, corresponds to the notion of nullity for symmetric and skew-symmetric matrices. In particular, as graphs (i.e., symmetric matrices over GF(2)) may be seen as a special class of delta-matroids, this distance measure generalizes the notion of nullity in this case. We characterize delta-matroids in terms of equicardinality of minimal sets with respect to inclusion (in addition, we obtain similar characterizations for matroids). In this way, we find that, e.g., the delta-matroids obtained after loop complementation and after pivot on a single element together with the original delta-matroid fulfill the property that two of them have equal "null space" while the third has a larger dimension. | Notes: | Hasselt Univ, Hasselt, Belgium. Transnat Univ Limburg, Diepenbeek, Belgium. Leiden Univ, Leiden Inst Adv Comp Sci, Leiden, Netherlands. | Keywords: | delta-matroid; local complementation; principal pivot transform; interlace polynomial; 4-regular graph;delta-matroid; local complementation; principal pivot transform; interlace polynomial; 4-regular graph | Document URI: | http://hdl.handle.net/1942/15199 | Link to publication/dataset: | http://arxiv.org/abs/1010.4497 | ISSN: | 0895-4801 | e-ISSN: | 1095-7146 | DOI: | 10.1137/110854692 | ISI #: | 000316868600030 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2014 |
Appears in Collections: | Research publications |
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nullity_loopc_dmatroid.pdf | 213.16 kB | Adobe PDF | View/Open |
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