Results 181 to 190 of about 382 (214)

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.
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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
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A parallel reduction of Hamiltonian cycle to Hamiltonian Path in tournaments

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, Mohamed El Haddad, Yannis Manoussakis, Miklos Santha   +3 more
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On Hamiltonian cycles as optimal p-cycles

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.
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Hamiltonian Cycles and Tight Cutsets

Graphs and Combinatorics
Let \(G\) be a graph. A cutset \(S\) of \(G\) is tight if \(|S|=c(G-S)\). The authors define a reduction step in \(G\) to be the deletion of all edges joining two vertices that lie together in a tight cutset, making each tight cutset independent. The (Hamiltonian) reduction \(R(G)\) of a 1-tough graph \(G\) is the iterative application of reduction ...
Viswanathan B. N, Douglas B. West
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Non‐Hamiltonian Cycles in Tournaments

Journal of Graph Theory
ABSTRACTA cycle is said to be directed if all its arcs have the same direction. Otherwise, it is said to be nondirected. A strong tournament is a tournament containing a directed path from any vertex to any other vertex. A tournament that is not strong is said to be reducible.
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Hamiltonian Cycles of Adjacent Triples

Studies in Applied Mathematics, 1980
A construction is given for ordering triples chosen from an ordered set of elements, so that each triple agrees with each neighbor in two of its members and has third member that is a neighbor of its neighbor's third member. Neighbors here are adjacent in order, and also the first is neighbor to the last among both elements and triples.
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On the Number of Hamiltonian Cycles in a Tournament

Combinatorics, Probability and Computing, 2005
It is shown that the maximum number \(C(n)\) of Hamiltonian cycles in a tournament of order \(n\) satisfies the inequaltiy \(C(n) < O(n^{3/2-\varepsilon}(n-1)!2^{-n})\), where \(\varepsilon = .2507\dots\). No claim is made concerning the sharpness of the bound.
Friedgut, Ehud, Kahn, Jeff
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Hamiltonian cycles in Dirac graphs

Combinatorica, 2009
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Bill Cuckler, Jeff Kahn 0001
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Disjoint Hamiltonian cycles in graphs [PDF]

Australas. J Comb., 1999
Let \(G\) be a \(2(k+1)\)-connected graph with the property \(uv \notin E(G)\) implies max\(\{ d(u),d(v) \} \geq n/2 + 2k\). It is shown that if \(\delta (G) \geq 4k+3\) then \(G\) contains \(k+1\) Hamiltonian cycles with no common edges. These cycles are constructed from the disjoint Hamiltonian cycles of a certain complete graph created from \(G ...
Guojun Li, Chuanping Chen
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