Hamiltonian Cycles in Signed and Multisigned Complete Graphs
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866915153837031424 |
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| author | Yan, Xiyong |
| author_facet | Yan, Xiyong |
| contents | A signed complete graph contains both positive and negative Hamiltonian cycles if and only if it also contains both positive and negative triangles. Otherwise, all Hamiltonian cycles are negative if and only if all triangles are negative and n is odd, while all Hamiltonian cycles are positive if and only if all triangles are negative and n is even, or all triangles are positive. Extending these results to multisigned complete graphs, we prove that such a graph contains at least two Hamiltonian cycles with different multisigns if and only if it contains at least two triangles with different multisigns. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_10612 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Hamiltonian Cycles in Signed and Multisigned Complete Graphs Yan, Xiyong Combinatorics Group Theory A signed complete graph contains both positive and negative Hamiltonian cycles if and only if it also contains both positive and negative triangles. Otherwise, all Hamiltonian cycles are negative if and only if all triangles are negative and n is odd, while all Hamiltonian cycles are positive if and only if all triangles are negative and n is even, or all triangles are positive. Extending these results to multisigned complete graphs, we prove that such a graph contains at least two Hamiltonian cycles with different multisigns if and only if it contains at least two triangles with different multisigns. |
| title | Hamiltonian Cycles in Signed and Multisigned Complete Graphs |
| topic | Combinatorics Group Theory |
| url | https://arxiv.org/abs/2502.10612 |