Results 211 to 220 of about 889,165 (240)

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 delaunay complexes

1989
We restate a conjecture concerning the existence of Hamiltonian cycles in graphs resulting from the Delaunay triangulation of point sets in the plane R2. We introduce the notion of Delaunay complex, the natural completion of a Delaunay triangulation. We show that Delaunay complexes are necessarily 3-connected.
Henry Crapo, Jean-Paul Laumond
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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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Hamiltonian Cycles in Regular Tournaments

Combinatorics, Probability and Computing, 2007
We show that every regular tournament on n vertices has at least n!/(2 + o(1)) n Hamiltonian cycles, thus answering a question of Thomassen [17] and providing a partial answer to a question of Friedgut and Kahn [7]. This compares to an upper bound of about O(n0.25n!/2 n ) for arbitrary tournaments due to Friedgut and Kahn ...
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Hamiltonian cycles in bipartite graphs

Combinatorica, 1995
Let \(G= (X, Y; E)\) be a balanced bipartite graph with vertex classes \(X\), \(Y\), edge set \(E\), and \(|X|= |Y|= n\). The balanced independence number \(\alpha^*(G)\) is defined to be \[ \max\{|A|: A\subseteq X\cup Y\wedge A\text{ is independent }\wedge \bigl||A\cap X|- |A\cap Y|\bigr|\leq 1\}.
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Hamiltonian Cycles in Products of Graphs

Canadian Mathematical Bulletin, 1975
Let V(G) and E(G) denote the vertex set and the edge set of a graph G; let Kn denote the complete graph with n vertices and let Kn, m denote the complete bipartite graph on n and m vertices. A Hamiltonian cycle (Hamiltonian path, respectively) in a graph G is a cycle (path, respectively) in G that contains all the vertices of G.
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