Nowhere-zero $3$-flows in Cayley graphs on solvable groups of twice square-free order
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866911543966302208 |
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| author | Ahanjideh, Milad Kovács, István |
| author_facet | Ahanjideh, Milad Kovács, István |
| contents | We verify Tutte's $3$-flow conjecture in the class of Cayley graphs on solvable groups of order $2n$, where $n$ is square-free. The proof relies on a new necessary and sufficient condition for a simple $5$-valent graph to admit a nowhere-zero $3$-flow in terms of a pseudoforest decomposition. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_24175 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Nowhere-zero $3$-flows in Cayley graphs on solvable groups of twice square-free order Ahanjideh, Milad Kovács, István Combinatorics 05C21, 05C25 We verify Tutte's $3$-flow conjecture in the class of Cayley graphs on solvable groups of order $2n$, where $n$ is square-free. The proof relies on a new necessary and sufficient condition for a simple $5$-valent graph to admit a nowhere-zero $3$-flow in terms of a pseudoforest decomposition. |
| title | Nowhere-zero $3$-flows in Cayley graphs on solvable groups of twice square-free order |
| topic | Combinatorics 05C21, 05C25 |
| url | https://arxiv.org/abs/2603.24175 |