Hamiltonicity of inhomogeneous random graphs
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866914437403770880 |
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| author | Garbe, Frederik Hladký, Jan Piga, Simón |
| author_facet | Garbe, Frederik Hladký, Jan Piga, Simón |
| contents | We provide a complete characterization of those graphons $W$ for which the inhomogeneous random graph $G(n,W)$ is asymptotically almost surely Hamiltonian. The characterization involves three conditions. Two of them constitute the characterization of $G(n,W)$ being a.a.s. connected, as was shown recently by Hladký and Viswanathan. The third condition captures a geometric obstacle which prevents $G(n,W)$ from having perfect fractional matchings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_00899 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hamiltonicity of inhomogeneous random graphs Garbe, Frederik Hladký, Jan Piga, Simón Combinatorics We provide a complete characterization of those graphons $W$ for which the inhomogeneous random graph $G(n,W)$ is asymptotically almost surely Hamiltonian. The characterization involves three conditions. Two of them constitute the characterization of $G(n,W)$ being a.a.s. connected, as was shown recently by Hladký and Viswanathan. The third condition captures a geometric obstacle which prevents $G(n,W)$ from having perfect fractional matchings. |
| title | Hamiltonicity of inhomogeneous random graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2604.00899 |