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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.01447 |
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| _version_ | 1866911769761415168 |
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| author | Christoph, Micha Nenadov, Rajko Petrova, Kalina |
| author_facet | Christoph, Micha Nenadov, Rajko Petrova, Kalina |
| contents | We show that if $n$ is odd and $p \ge C \log n / n$, then with high probability Hamilton cycles in $G(n,p)$ span its cycle space. More generally, we show this holds for a class of graphs satisfying certain natural pseudorandom properties. The proof is based on a novel idea of parity-switchers, which can be thought of as analogues of absorbers in the context of cycle spaces. As another application of our method, we show that Hamilton cycles in a near-Dirac graph $G$, that is, a graph $G$ with odd $n$ vertices and minimum degree $n/2 + C$ for sufficiently large constant $C$, span its cycle space. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_01447 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | The Hamilton space of pseudorandom graphs Christoph, Micha Nenadov, Rajko Petrova, Kalina Combinatorics We show that if $n$ is odd and $p \ge C \log n / n$, then with high probability Hamilton cycles in $G(n,p)$ span its cycle space. More generally, we show this holds for a class of graphs satisfying certain natural pseudorandom properties. The proof is based on a novel idea of parity-switchers, which can be thought of as analogues of absorbers in the context of cycle spaces. As another application of our method, we show that Hamilton cycles in a near-Dirac graph $G$, that is, a graph $G$ with odd $n$ vertices and minimum degree $n/2 + C$ for sufficiently large constant $C$, span its cycle space. |
| title | The Hamilton space of pseudorandom graphs |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2402.01447 |