Results 291 to 300 of about 55,873 (316)
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On the Number of Hamiltonian Cycles in a Tournament
Combinatorics, Probability and Computing, 2005It 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.
Ehud Friedgut, Jeff Kahn
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On the number of Hamiltonian cycles in triangulations
Journal of Graph Theory, 1988AbstractIt is proved that if a planar triangulation different from K3 and K4 contains a Hamiltonian cycle, then it contains at least four of them. Together with the result of Hakimi, Schmeichel, and Thomassen [2], this yields that, for n ⩾ 12, the minimum number of Hamiltonian cycles in a Hamiltonian planar triangulation on n vertices is four.
Dainis Zeps, Jan Kratochvíl
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Hamiltonian Cycles of Adjacent Triples
Studies in Applied Mathematics, 1980A 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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Hamiltonian Cycles in Products of Graphs
Canadian Mathematical Bulletin, 1975Let 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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Hamiltonian cycles in bipartite graphs
Combinatorica, 1995Let \(G= (X, Y; E)\) 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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Halide perovskites enable polaritonic XY spin Hamiltonian at room temperature
Nature Materials, 2022Louis Haeberlé, , Dafei Jin
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Floquet Hamiltonian engineering of an isolated many-body spin system
Science, 2021Sebastian Geier +2 more
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Hamiltonian formulation of general relativity and post-Newtonian dynamics of compact binaries
Living Reviews in Relativity, 2018Piotr Jaranowski
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