Chordal matroids arising from generalized parallel connections
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911861889302528 |
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| author | Douthitt, James Dylan Oxley, James |
| author_facet | Douthitt, James Dylan Oxley, James |
| contents | A graph is chordal if every cycle of length at least four has a chord. In 1961, Dirac characterized chordal graphs as those graphs that can be built from complete graphs by repeated clique-sums. Generalizing this, we consider the class of simple $GF(q)$-representable matroids that can be built from projective geometries over $GF(q)$ by repeated generalized parallel connections across projective geometries. We show that this class of matroids is closed under induced minors. We characterize the class by its forbidden induced minors; the case when $q=2$ is distinctive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_07514 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Chordal matroids arising from generalized parallel connections Douthitt, James Dylan Oxley, James Combinatorics A graph is chordal if every cycle of length at least four has a chord. In 1961, Dirac characterized chordal graphs as those graphs that can be built from complete graphs by repeated clique-sums. Generalizing this, we consider the class of simple $GF(q)$-representable matroids that can be built from projective geometries over $GF(q)$ by repeated generalized parallel connections across projective geometries. We show that this class of matroids is closed under induced minors. We characterize the class by its forbidden induced minors; the case when $q=2$ is distinctive. |
| title | Chordal matroids arising from generalized parallel connections |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2306.07514 |