Signs of Hamiltonian Circles in Simple Plane Signed Graphs
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2026
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866915815747485696 |
|---|---|
| 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 |