On the Complexity of Determining Whether there is a Unique Hamiltonian Cycle or Path
Computational Complexity
2022-05-13 v1
Abstract
The decision problems of the existence of a Hamiltonian cycle or of a Hamiltonian path in a given graph, and of the existence of a truth assignment satisfying a given Boolean formula , are well-known {\it NP}-complete problems. Here we study the problems of the {\it uniqueness} of a Hamiltonian cycle or path in an undirected, directed or oriented graph, and show that they have the same complexity, up to polynomials, as the problem U-SAT of the uniqueness of an assignment satisfying . As a consequence, these Hamiltonian problems are {\it NP}-hard and belong to the class~{\it DP}, like U-SAT.
Keywords
Cite
@article{arxiv.2205.05782,
title = {On the Complexity of Determining Whether there is a Unique Hamiltonian Cycle or Path},
author = {Olivier Hudry and Antoine Lobstein},
journal= {arXiv preprint arXiv:2205.05782},
year = {2022}
}