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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2502.14853 |
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| _version_ | 1866911305616588800 |
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| author | Gao, Wanting Chen, Xudong |
| author_facet | Gao, Wanting Chen, Xudong |
| contents | We investigate the $H$-property for step-graphons. Specifically, we sample graphs $G_n$ on $n$ nodes from a step-graphon and evaluate the probability that $G_n$ has a Hamiltonian decomposition in the asymptotic regime as $n\to\infty$. It has been shown that for almost all step-graphons, this probability converges to either zero or one. We focus in this paper on the residual case where the zero-one law does not apply. We show that the limit of the probability still exists and provide an explicit expression of it. We present a complete proof of the result and validate it through numerical studies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_14853 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the $H$-property for Step-graphons: The Residual Case Gao, Wanting Chen, Xudong Systems and Control We investigate the $H$-property for step-graphons. Specifically, we sample graphs $G_n$ on $n$ nodes from a step-graphon and evaluate the probability that $G_n$ has a Hamiltonian decomposition in the asymptotic regime as $n\to\infty$. It has been shown that for almost all step-graphons, this probability converges to either zero or one. We focus in this paper on the residual case where the zero-one law does not apply. We show that the limit of the probability still exists and provide an explicit expression of it. We present a complete proof of the result and validate it through numerical studies. |
| title | On the $H$-property for Step-graphons: The Residual Case |
| topic | Systems and Control |
| url | https://arxiv.org/abs/2502.14853 |