On orientations preserving edge-connectivity in infinite graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909830868893696 |
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| author | Aurichi, Leandro Júnior, Paulo Magalhães Pinto, Guilherme Eduardo |
| author_facet | Aurichi, Leandro Júnior, Paulo Magalhães Pinto, Guilherme Eduardo |
| contents | We prove that every 2k-edge-connected graph with countably many edge-ends admits a k-arc-connected orientation, extending the previous result by Assem, Koloschin and Pitz that also assumed the hypothesis of the graph being locally finite. We prove that, if every locally finite graph has a well-balanced orientation, so does every graph. Lastly, we explore an alternative to the Nash-Williams Orientation Conjecture via topological paths, and prove that it is true for every finitely separated graph. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_06449 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On orientations preserving edge-connectivity in infinite graphs Aurichi, Leandro Júnior, Paulo Magalhães Pinto, Guilherme Eduardo Combinatorics General Topology 05C63 (Primary) 05C38, 05C40, 54H99(Secondary) We prove that every 2k-edge-connected graph with countably many edge-ends admits a k-arc-connected orientation, extending the previous result by Assem, Koloschin and Pitz that also assumed the hypothesis of the graph being locally finite. We prove that, if every locally finite graph has a well-balanced orientation, so does every graph. Lastly, we explore an alternative to the Nash-Williams Orientation Conjecture via topological paths, and prove that it is true for every finitely separated graph. |
| title | On orientations preserving edge-connectivity in infinite graphs |
| topic | Combinatorics General Topology 05C63 (Primary) 05C38, 05C40, 54H99(Secondary) |
| url | https://arxiv.org/abs/2510.06449 |