Hamiltonian Sets of Polygonal Paths in Assembly Graphs
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917321886400512 |
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| author | Guterman, A. Jonoska, N. Kreines, E. Maksaev, A. Ostroukhova, N. |
| author_facet | Guterman, A. Jonoska, N. Kreines, E. Maksaev, A. Ostroukhova, N. |
| contents | We provide four equivalent combinatorial conditions for a simple assembly graph (rigid vertex graph where all vertices are of degree 1 or 4) to have the largest number of Hamiltonian sets of polygonal paths relative its size. These conditions serve to prove the conjecture that such maximum, which is equal to $F_{2n+1}-1$, where $F_k$ denotes the $k$th Fibonacci number, is achieved only for special assembly graphs, called tangled cords. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_07296 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hamiltonian Sets of Polygonal Paths in Assembly Graphs Guterman, A. Jonoska, N. Kreines, E. Maksaev, A. Ostroukhova, N. Combinatorics Primary 05C10, Secondary 57M15, 68R15 We provide four equivalent combinatorial conditions for a simple assembly graph (rigid vertex graph where all vertices are of degree 1 or 4) to have the largest number of Hamiltonian sets of polygonal paths relative its size. These conditions serve to prove the conjecture that such maximum, which is equal to $F_{2n+1}-1$, where $F_k$ denotes the $k$th Fibonacci number, is achieved only for special assembly graphs, called tangled cords. |
| title | Hamiltonian Sets of Polygonal Paths in Assembly Graphs |
| topic | Combinatorics Primary 05C10, Secondary 57M15, 68R15 |
| url | https://arxiv.org/abs/2603.07296 |