Name
Abstract | ||
|---|---|---|
Vf-safe delta-matroids have the desirable property of behaving well under certain duality operations. Several important classes of delta-matroids are known to be vf-safe, including the class of ribbon-graphic delta-matroids, which is related to the class of ribbon graphs or embedded graphs in the same way that graphic matroids correspond to graphs. In this paper, we characterize vf-safe delta-matroids and ribbon-graphic delta-matroids by finding the minimal obstructions, called excluded 3-minors, to membership in the class. We find the unique (up to twisted duality) excluded 3-minor within the class of set systems for the class of vf-safe delta-matroids. In the literature, binary delta-matroids appear in many different guises, with appropriate notions of minor operations equivalent to that of 3-minors, perhaps most notably as graphs with vertex minors. We give a direct explanation of this equivalence and show that some well-known results may be expressed in terms of 3-minors. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1016/j.aam.2019.04.006 | Advances in Applied Mathematics |
Keywords | DocType | Volume |
05B35 | Journal | 126 |
ISSN | Citations | PageRank |
0196-8858 | 0 | 0.34 |
References | Authors | |
8 | 3 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Joseph E. Bonin | 1 | 53 | 16.74 |
| Carolyn Chun | 2 | 25 | 8.25 |
| S. D. Noble | 3 | 83 | 9.56 |