Small Spectral Gap in the Combinatorial Laplacian Implies Hamiltonian
Steve Butler,Fan Chung +1 more
Reads0
Chats0
TLDR
In this article, a sufficient condition for a graph being Hamiltonian is that the nontrivial eigenvalues of the combinatorial Laplacian are sufficiently close to the average degree of the graph.Abstract:
We consider the spectral and algorithmic aspects of the problem of finding a Hamil- tonian cycle in a graph. We show that a sufficient condition for a graph being Hamiltonian is that the nontrivial eigenvalues of the combinatorial Laplacian are sufficiently close to the average degree of the graph. An algorithm is given for the problem of finding a Hamiltonian cycle in graphs with bounded spectral gaps which has complexity of order n c ln n .read more
Citations
More filters
Book
Proceedings of the International Congress of Mathematicians
TL;DR: The main topics of eohomologieal investigation in Algebraic Geometry, as they appear at present, can be found in this article, with the main focus on the Weil cohomology.
Journal ArticleDOI
Quantum algorithms for topological and geometric analysis of data
TL;DR: In this article, quantum machine learning algorithms for calculating Betti numbers in persistent homology and for finding eigenvectors and eigenvalues of the combinatorial Laplacian are presented.
Journal ArticleDOI
Spectral radius and Hamiltonicity of graphs
TL;DR: In this paper, it was shown that if G is a graph of order n and μ (G ) is the largest eigenvalue of its adjacency matrix, then G does not contain a Hamiltonian cycle unless G = K n - 1 + e + v.
Journal ArticleDOI
Recent Advances on the Hamiltonian Problem: Survey III
TL;DR: This article is intended as a survey, updating earlier surveys in the area, and contains some material on closely related topics such as traceable, pancyclic and Hamiltonian connected graphs.
References
More filters
Book ChapterDOI
Reducibility Among Combinatorial Problems
TL;DR: The work of Dantzig, Fulkerson, Hoffman, Edmonds, Lawler and other pioneers on network flows, matching and matroids acquainted me with the elegant and efficient algorithms that were sometimes possible.
Book
The Probabilistic Method
TL;DR: A particular set of problems - all dealing with “good” colorings of an underlying set of points relative to a given family of sets - is explored.
Journal ArticleDOI
The Traveling-Salesman Problem and Minimum Spanning Trees
Michael Held,Richard M. Karp +1 more
TL;DR: It is shown that maxπwπ = C* precisely when a certain well-known linear program has an optimal solution in integers.
Book ChapterDOI
Exact algorithms for NP-hard problems: a survey
TL;DR: The list of discussed NP-complete problems includes the traveling salesman problem, scheduling under precedence constraints, satisfiability, knapsack, graph coloring, independent sets in graphs, bandwidth of a graph, and many more as discussed by the authors.