Infinite random graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866908781851443200 |
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| author | Kostana, Ziemowit Swaczyna, Jarosław Widz, Agnieszka |
| author_facet | Kostana, Ziemowit Swaczyna, Jarosław Widz, Agnieszka |
| contents | We study countable graphs that -- up to isomorphism and with probability one -- arise from a random process, in a similar fashion as the Rado graph. Unlike in the classical case, we do not require that probabilities assigned to pairs of points are all equal. We give examples of such generalized random graphs, and show that the class of graphs under consideration has a two-element basis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16013 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Infinite random graphs Kostana, Ziemowit Swaczyna, Jarosław Widz, Agnieszka Combinatorics 05C80, 05C63, 60C05 We study countable graphs that -- up to isomorphism and with probability one -- arise from a random process, in a similar fashion as the Rado graph. Unlike in the classical case, we do not require that probabilities assigned to pairs of points are all equal. We give examples of such generalized random graphs, and show that the class of graphs under consideration has a two-element basis. |
| title | Infinite random graphs |
| topic | Combinatorics 05C80, 05C63, 60C05 |
| url | https://arxiv.org/abs/2601.16013 |