Hamiltonian Sets of Polygonal Paths in Assembly Graphs
Abstract 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 to its size. These conditions serve to prove the conjecture that such a 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.
Authors
- E. M. Kreines (ORCID: https://orcid.org/0000-0003-4059-001X)
- A. M. Maksaev (ORCID: https://orcid.org/0000-0002-9971-4788)
- N. Jonoska
- Alexander Guterman
- Natalia Ostroukhova
Institutions
- National Research University Higher School of Economics (RU)
- Ben-Gurion University of the Negev (IL)
- Bar-Ilan University (IL)
- Tel Aviv University (IL)
- University of South Florida (US)
- Moscow Center For Continuous Mathematical Education (RU)
- Applied Mathematics (United States) (US)
Publication Details
- Journal
- Proceedings of the Edinburgh Mathematical Society
- Published
- 2026-03-05
- DOI
- https://doi.org/10.1017/s0013091526101357
- Primary Topic
- Structural Analysis and Optimization
- Type
- article
- Field-Weighted Citation Impact
- 0.00
Funders
- National Science Foundation
- W. M. Keck Foundation
- Israel Science Foundation
- Tel Aviv University
- National Research University Higher School of Economics