Realization and classification of Hamiltonian-circle multisigns
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866909920341786624 |
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| author | Yan, Xiyong |
| author_facet | Yan, Xiyong |
| contents | We investigate the multisigns of Hamiltonian circles in the multisigned complete graph \(Σ_n := (K_n, σ, \mathbb{F}_2^m)\). The \emph{multisign} of a circle \(C\) is defined as the sum \[ σ(C) := \sum_{e \in E(C)} σ(e). \] For a fixed \(m\) and sufficiently large \(n\), we show that the set of multisigns of Hamiltonian circles \[ \{σ(H) : H \text{ is a Hamiltonian circle of } Σ_n)\} \] forms either a subspace, an affine subspace, or the entire space \(\mathbb{F}_2^m\), except in certain exceptional cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_18759 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Realization and classification of Hamiltonian-circle multisigns Yan, Xiyong Combinatorics We investigate the multisigns of Hamiltonian circles in the multisigned complete graph \(Σ_n := (K_n, σ, \mathbb{F}_2^m)\). The \emph{multisign} of a circle \(C\) is defined as the sum \[ σ(C) := \sum_{e \in E(C)} σ(e). \] For a fixed \(m\) and sufficiently large \(n\), we show that the set of multisigns of Hamiltonian circles \[ \{σ(H) : H \text{ is a Hamiltonian circle of } Σ_n)\} \] forms either a subspace, an affine subspace, or the entire space \(\mathbb{F}_2^m\), except in certain exceptional cases. |
| title | Realization and classification of Hamiltonian-circle multisigns |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2511.18759 |