Signs of Hamiltonian Circles in Simple Plane Signed Graphs
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| Soggetti: | |
| Accesso online: | |
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| _version_ | 1866915815747485696 |
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| author | Yan, Xiyong |
| author_facet | Yan, Xiyong |
| contents | We study which signs can occur among Hamiltonian circles in simple plane signed graphs. Using a face-based viewpoint, we relate the sign of a Hamiltonian circle to the product of the signs of the faces inside it, and we introduce co-Hamiltonian sequences. This yields a criterion for the existence of opposite-sign Hamiltonian circles via two co-Hamiltonian sequences with opposite face-products. Motivated by signed grid graphs, we develop local structural theorems that allow one to certify the existence of both signs without explicitly constructing the full sequences, including a ladder-type configuration where toggling along two $4$-circles produces Hamiltonian circles of opposite sign, as well as hexagon configurations that realize both signs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21530 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Signs of Hamiltonian Circles in Simple Plane Signed Graphs Yan, Xiyong Combinatorics We study which signs can occur among Hamiltonian circles in simple plane signed graphs. Using a face-based viewpoint, we relate the sign of a Hamiltonian circle to the product of the signs of the faces inside it, and we introduce co-Hamiltonian sequences. This yields a criterion for the existence of opposite-sign Hamiltonian circles via two co-Hamiltonian sequences with opposite face-products. Motivated by signed grid graphs, we develop local structural theorems that allow one to certify the existence of both signs without explicitly constructing the full sequences, including a ladder-type configuration where toggling along two $4$-circles produces Hamiltonian circles of opposite sign, as well as hexagon configurations that realize both signs. |
| title | Signs of Hamiltonian Circles in Simple Plane Signed Graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2602.21530 |