Closure property of contraction-depth of matroids
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911049479880704 |
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| author | Brianski, Marcin Kral, Daniel Lamaison, Ander |
| author_facet | Brianski, Marcin Kral, Daniel Lamaison, Ander |
| contents | Contraction$^*$-depth is a matroid depth parameter analogous to tree-depth of graphs. We establish the matroid analogue of the classical graph theory result asserting that the tree-depth of a graph $G$ is the minimum height of a rooted forest whose closure contains $G$ by proving the following for every matroid $M$ (except the trivial case when $M$ consists of loops and coloops only): the contraction$^*$-depth of $M$ plus one is equal to the minimum contraction-depth of a matroid containing $M$ as a restriction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01945 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Closure property of contraction-depth of matroids Brianski, Marcin Kral, Daniel Lamaison, Ander Combinatorics Discrete Mathematics Contraction$^*$-depth is a matroid depth parameter analogous to tree-depth of graphs. We establish the matroid analogue of the classical graph theory result asserting that the tree-depth of a graph $G$ is the minimum height of a rooted forest whose closure contains $G$ by proving the following for every matroid $M$ (except the trivial case when $M$ consists of loops and coloops only): the contraction$^*$-depth of $M$ plus one is equal to the minimum contraction-depth of a matroid containing $M$ as a restriction. |
| title | Closure property of contraction-depth of matroids |
| topic | Combinatorics Discrete Mathematics |
| url | https://arxiv.org/abs/2311.01945 |