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Solving the Hamiltonian Cycle Problem using a Quantum Computer
Australasian Computer Science Week, 2019We 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+3 more
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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+2 more
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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+2 more
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The Hamiltonian Cycle and Travelling Salesman Problems in cP Systems
Fundamenta Informaticae, 2019The 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
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Finding Hamiltonian Cycle in Graphs of Bounded Treewidth
The Sea, 2018The 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
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Alternating Hamiltonian cycles
Israel Journal of Mathematics, 1976Coloar 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
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The Square of a Hamiltonian Cycle
SIAM Journal on Discrete Mathematics, 1994Let 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
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A parallel reduction of Hamiltonian cycle to Hamiltonian Path in tournaments [PDF]
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+4 more
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On Hamiltonian cycles in the FCC grid
Computers & Graphics, 2020Abstract 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
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A Remark on Hamiltonian Cycles
Mathematische Nachrichten, 1992AbstractLet 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.
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On Hamiltonian cycles as optimal p-cycles [PDF]
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.
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