Hamiltonian Sets of Polygonal Paths in Assembly Graphs
Combinatorics
2026-03-10 v1
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 its size. These conditions serve to prove the conjecture that such maximum, which is equal to , where denotes the th Fibonacci number, is achieved only for special assembly graphs, called tangled cords.
Keywords
Cite
@article{arxiv.2603.07296,
title = {Hamiltonian Sets of Polygonal Paths in Assembly Graphs},
author = {A. Guterman and N. Jonoska and E. Kreines and A. Maksaev and N. Ostroukhova},
journal= {arXiv preprint arXiv:2603.07296},
year = {2026}
}