Results 291 to 300 of about 3,095,070 (339)

Solving the Hamiltonian Cycle Problem using a Quantum Computer

Australasian Computer Science Week, 2019
We review existing quantum computational methods for solving the Hamiltonian cycle problem in different computational frameworks such as quantum circuits, quantum walks and adiabatic quantum computation.
A. Mahasinghe, R. Hua, M. Dinneen, Rajni Goyal   +3 more
semanticscholar   +1 more source

Finding Hamiltonian Cycles

Science, 1996
L. Adleman has proposed and demonstrated a highly novel approach using DNA and the tools of molecular biology to solve the famous Hamiltonian cycle problem (HCP) of computer science: Given a directed graph on N vertices ( N cities and a set of R ≤ N 2 one-way roads connecting the cities), does there exist a subset of the roads in which a tour of the ...
Martin Lades, Eric Lewin Altschuler, Richard Stong   +2 more
openaire   +2 more sources

The Hamiltonian Cycle and Travelling Salesman Problems in cP Systems

Fundamenta Informaticae, 2019
The Hamiltonian Cycle Problem (HCP) and Travelling Salesman Problem (TSP) are long-standing and well-known NP-hard problems. The HCP is concerned with finding paths through a given graph such that those paths visit each node exactly once after the start,
J. Cooper, Radu Nicolescu
semanticscholar   +1 more source

Finding Hamiltonian Cycle in Graphs of Bounded Treewidth

The Sea, 2018
The notion of treewidth, introduced by Robertson and Seymour in their seminal Graph Minors series, turned out to have tremendous impact on graph algorithmics.
Michal Ziobro, Marcin Pilipczuk
semanticscholar   +1 more source

Alternating Hamiltonian cycles

Israel Journal of Mathematics, 1976
Coloar the edges of a complete graph with n vertices in such a way that no vertex is on more than k edges of the same colour . We prove that for every k there is a constant c ksuch that if n > ck then there is a Hamiltonian cycle with adjacent edges having different colours . We prove a number of other results in the same vein and mention some unsolved
Paul Erdős, Béla Bollobás
openaire   +2 more sources

The Square of a Hamiltonian Cycle

SIAM Journal on Discrete Mathematics, 1994
Let C be a cycle. The square of C is the graph obtained by joining every pair of vertices of distance 2 in C. Let G be a graph on n vertices with minimum degree $\delta(G)$. This paper proves that, if $\delta(G)\geq \frac{5}{7}n$ , then G contains the square of a Hamiltonian cycle.
Roland Haggkvist, Genghua Fan
openaire   +2 more sources

A parallel reduction of Hamiltonian cycle to Hamiltonian Path in tournaments [PDF]

Journal of Algorithms, 1993
We propose a parallel algorithm which reduces the problem of computing Hamiltonian cycles in tournaments to the problem of computing Hamiltonian paths. The running time of our algorithm is O(log n) using O(n2/log n) processors on a CRCW PRAM, and O(log n log log n) on an EREW PRAM using O(n2/log n log log n) processors.
Evripidis Bampis, Miklos Santha, Miklos Santha, M. El Haddad, Yannis Manoussakis   +4 more
openaire   +2 more sources

On Hamiltonian cycles in the FCC grid

Computers & Graphics, 2020
Abstract The face centered cubic (FCC) grid is a space-filling grid, one of the alternatives to the traditional cubic one. We show that there are five Hamiltonian cycles (non-equivalent up to rotation and symmetry), connecting the faces of a voxel in the FCC grid.
Lidija Comic, Paola Magillo
openaire   +2 more sources

A Remark on Hamiltonian Cycles

Mathematische Nachrichten, 1992
AbstractLet G be an undirected and simple graph on n vertices. Let ω, α and χ denote the number of components, the independence number and the connectivity number of G. G is called a 1‐tough graph if ω(G – S) ⩽ |S| for any subset S of V(G) such that ω(G − S) > 1.
openaire   +2 more sources

On Hamiltonian cycles as optimal p-cycles [PDF]

IEEE Communications Letters, 2005
Using Hamiltonian p-cycles, it can be shown that p-cycle design is able to reach the logical redundancy bound of 1/(d~-1) where d~ is the average node degree. We formulate two conditions on which the design is able to reach this bound if and only if Hamiltonian p-cycles are used.
openaire   +1 more source