Arithmetical Semirings
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2016
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| _version_ | 1866913238783885312 |
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| author | Aldi, Marco |
| author_facet | Aldi, Marco |
| contents | We study the number of connected graphs with $n$ vertices that cannot be written as the cartesian product of two graphs with fewer vertices. We give an upper bound which implies that for large $n$ almost all graphs are both connected and cartesian prime. For graphs with an even number of vertices, a full asymptotic expansion is obtained. Our method, inspired by Knopfmacher's theory of arithmetical semigroups, is based on reduction to Wright's asymptotic expansion for the number of connected graphs with $n$ vertices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1605_08640 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Arithmetical Semirings Aldi, Marco Combinatorics We study the number of connected graphs with $n$ vertices that cannot be written as the cartesian product of two graphs with fewer vertices. We give an upper bound which implies that for large $n$ almost all graphs are both connected and cartesian prime. For graphs with an even number of vertices, a full asymptotic expansion is obtained. Our method, inspired by Knopfmacher's theory of arithmetical semigroups, is based on reduction to Wright's asymptotic expansion for the number of connected graphs with $n$ vertices. |
| title | Arithmetical Semirings |
| topic | Combinatorics |
| url | https://arxiv.org/abs/1605.08640 |