Results 281 to 290 of about 55,873 (316)

Alternating Hamiltonian cycles

Israel Journal of Mathematics, 1976
For natural numbers \(n\) and \(d\), let \(K_n(\Delta_c \leq d)\) denote a complete graph of order \(n\) whose edges are colored so that no vertex belongs to more than \(d\) edges of the same color, and where \(\Delta_c\) is the maximal degree in the subgraph formed by the edges of color \(c\). D. E. Daykin proved that if \(d=2\) and \(n \geq 6\), then
Paul Erdős, Béla Bollobás
openaire   +2 more sources

The Square of a Hamiltonian Cycle

SIAM Journal on Discrete Mathematics, 1994
All graphs considered in this paper are simple and undirected. For a given graph \(G= (V,E)\) we denote by \(\delta(G)\) the minimum degree of \(G\). A \(k\)-chord of a cycle \(C\) is an edge joining two vertices of distance \(k\) on \(C\). The \(k\)th power of \(C\) is the graph obtained by joining every pair of vertices with distance at most \(k\) on
Roland Haggkvist, Genghua Fan
openaire   +2 more sources

On Hamiltonian cycles and Hamiltonian paths

Information Processing Letters, 2005
A Hamiltonian cycle is a spanning cycle in a graph, i.e., a cycle through every vertex, and a Hamiltonian path is a spanning path. In this paper we present two theorems stating sufficient conditions for a graph to possess Hamiltonian cycles and Hamiltonian paths.
Mohammad Kaykobad, M. Sohel Rahman
openaire   +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

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   +3 more sources

Detecting Hamiltonian cycles

Applied Mathematics and Computation, 1992
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +3 more sources

Hamiltonian Cycles and Markov Chains

Mathematics of Operations Research, 1994
In this paper we derive new characterizations of the Hamiltonian cycles of a directed graph, and a new LP-relaxation of the Traveling Salesman Problem. Our results are obtained via an embedding of these combinatorial optimization problems in suitably perturbed controlled Markov chains.
Filar, JA, Krass, D
openaire   +4 more sources

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

Journal of Algorithms, 1993
Summary: 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 \(O(n^2/\log n)\) processors on a CRCW PRAM, and \(O(\log n \log \log n)\) on an EREW PRAM using \(O(n^2/ \log n \log \log n ...
Evripidis Bampis, Miklos Santha, Miklos Santha, M. El Haddad, Yannis Manoussakis   +4 more
openaire   +2 more sources

Degeneration of Hamiltonian monodromy cycles

Nonlinearity, 1993
This paper is concerned with the global topology of solution trajectories to integrable Hamiltonian systems near ``degenerate'' critical points of the energy-momentum map. The present study is restricted to two examples, the Kirchhoff top and the spherical pendulum in an axially symmetric quadratic potential.
L Bates, Maorong Zou
openaire   +3 more sources