The classification of homomorphism homogeneous oriented graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866915719374962688 |
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| author | Pavlica, Bojana Pech, Christian Pech, Maja |
| author_facet | Pavlica, Bojana Pech, Christian Pech, Maja |
| contents | The modern theory of homogeneous structures begins with the work of Roland Fraïssé. The theory developed in the last seventy years is placed in the border area between combinatorics, model theory, algebra, and analysis. We turn our attention to its combinatorial pillar, namely, the work on the classification of structures for given homogeneity types, and focus onto the homomorphism homogeneous ones, introduced in 2006 by Cameron and Nešetřil. An oriented graph is called homomorphism homogeneous if every homomorphism between finite induced subgraphs extends to an endomorphism. In this paper we present a complete classification of the countable homomorphism homogeneous oriented graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04393 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The classification of homomorphism homogeneous oriented graphs Pavlica, Bojana Pech, Christian Pech, Maja Combinatorics Logic 05C20 (Primary) 05C63 (Secondary) The modern theory of homogeneous structures begins with the work of Roland Fraïssé. The theory developed in the last seventy years is placed in the border area between combinatorics, model theory, algebra, and analysis. We turn our attention to its combinatorial pillar, namely, the work on the classification of structures for given homogeneity types, and focus onto the homomorphism homogeneous ones, introduced in 2006 by Cameron and Nešetřil. An oriented graph is called homomorphism homogeneous if every homomorphism between finite induced subgraphs extends to an endomorphism. In this paper we present a complete classification of the countable homomorphism homogeneous oriented graphs. |
| title | The classification of homomorphism homogeneous oriented graphs |
| topic | Combinatorics Logic 05C20 (Primary) 05C63 (Secondary) |
| url | https://arxiv.org/abs/2403.04393 |