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| Main Author: | |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2406.06931 |
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| _version_ | 1866909440654966784 |
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| author | Lyskov, Denis |
| author_facet | Lyskov, Denis |
| contents | We study Hamiltonian paths and cycles in undirected graphs from an operadic viewpoint. We show that the graphical collection $\mathsf{Ham}$ encoding directed Hamiltonian paths in connected graphs admits an operad-like structure, called a contractad. Similarly, we construct the graphical collection of Hamiltonian cycles $\mathsf{CycHam}$ that forms a right module over the contractad $\mathsf{Ham}$. We use the machinery of contractad generating series for counting Hamiltonian paths/cycles for particular types of graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_06931 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Operadic structure on Hamiltonian paths and cycles Lyskov, Denis Combinatorics K-Theory and Homology We study Hamiltonian paths and cycles in undirected graphs from an operadic viewpoint. We show that the graphical collection $\mathsf{Ham}$ encoding directed Hamiltonian paths in connected graphs admits an operad-like structure, called a contractad. Similarly, we construct the graphical collection of Hamiltonian cycles $\mathsf{CycHam}$ that forms a right module over the contractad $\mathsf{Ham}$. We use the machinery of contractad generating series for counting Hamiltonian paths/cycles for particular types of graphs. |
| title | Operadic structure on Hamiltonian paths and cycles |
| topic | Combinatorics K-Theory and Homology |
| url | https://arxiv.org/abs/2406.06931 |