Singular fibres of the momentum mapping for integrable Hamiltonian systems.
Horst Knörrer (1984)
Journal für die reine und angewandte Mathematik
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Horst Knörrer (1984)
Journal für die reine und angewandte Mathematik
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Thomas Bartsch, Michel Willem (1994)
Journal für die reine und angewandte Mathematik
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E. Zenhder (1975)
Publications mathématiques et informatique de Rennes
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Boris Khesin (1993)
Recherche Coopérative sur Programme n°25
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Franz Rothe (1984)
Journal für die reine und angewandte Mathematik
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Gary Chartrand, S. F. Kapoor (1974)
Colloquium Mathematicae
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Jens-P. Bode, Anika Fricke, Arnfried Kemnitz (2015)
Discussiones Mathematicae Graph Theory
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In 1980 Bondy [2] proved that a (k+s)-connected graph of order n ≥ 3 is traceable (s = −1) or Hamiltonian (s = 0) or Hamiltonian-connected (s = 1) if the degree sum of every set of k+1 pairwise nonadjacent vertices is at least ((k+1)(n+s−1)+1)/2. It is shown in [1] that one can allow exceptional (k+ 1)-sets violating this condition and still implying the considered Hamiltonian property. In this note we generalize this result for s = −1 and s = 0 and graphs that fulfill a certain connectivity...
Demovič, A. (1995)
Acta Mathematica Universitatis Comenianae. New Series
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Jianxiang Cao, Minyong Shi, Lihua Feng (2016)
Discussiones Mathematicae Graph Theory
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The balanced hypercube BHn, defined by Wu and Huang, is a variant of the hypercube network Qn, and has been proved to have better properties than Qn with the same number of links and processors. For a bipartite graph G = (V0 ∪ V1,E), we say G is edge-hyper-Hamiltonian laceable if it is Hamiltonian laceable, and for any vertex v ∈ Vi, i ∈ {0, 1}, any edge e ∈ E(G − v), there is a Hamiltonian path containing e in G − v between any two vertices of V1−i. In this paper, we prove that BHn...
Henryk Żołądek (2011)
Banach Center Publications
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The first and the second Painlevé equations are explicitly Hamiltonian with time dependent Hamilton function. By a natural extension of the phase space one gets corresponding autonomous Hamiltonian systems in ℂ⁴. We prove that the latter systems do not have any additional algebraic first integral. In the proof equations in variations with respect to a parameter are used.
Kewen Zhao, Ronald J. Gould (2010)
Colloquium Mathematicae
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An independent set S of a graph G is said to be essential if S has a pair of vertices that are distance two apart in G. In 1994, Song and Zhang proved that if for each independent set S of cardinality k+1, one of the following condition holds: (i) there exist u ≠ v ∈ S such that d(u) + d(v) ≥ n or |N(u) ∩ N(v)| ≥ α (G); (ii) for any distinct u and v in S, |N(u) ∪ N(v)| ≥ n - max{d(x): x ∈ S}, then G is Hamiltonian. We prove that if for each...
D. Z. Du, D. F. Hsu (1989)
Banach Center Publications
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Delshams, Amadeu, Seara, Tere M. (1997)
Mathematical Physics Electronic Journal [electronic only]
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Jill R. Faudree, Ralph J. Faudree, Ronald J. Gould, Michael S. Jacobson, Colton Magnant (2010)
Discussiones Mathematicae Graph Theory
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The Chvátal-Erdös theorems imply that if G is a graph of order n ≥ 3 with κ(G) ≥ α(G), then G is hamiltonian, and if κ(G) > α(G), then G is hamiltonian-connected. We generalize these results by replacing the connectivity and independence number conditions with a weaker minimum degree and independence number condition in the presence of sufficient connectivity. More specifically, it is noted that if G is a graph of order n and k ≥ 2 is a positive integer such that κ(G) ≥ k, δ(G) >...
Popescu, Paul, Popescu, Marcela (2002)
Balkan Journal of Geometry and its Applications (BJGA)
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Bing Wang, Xinghu Wang, Honghua Wang (2016)
Kybernetika
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In this paper, the output synchronization control is considered for multi-agent port-Hamiltonian systems with link dynamics. By using Hamiltonian energy function and Casimir function comprehensively, the design method is proposed to overcome the difficulties taken by link dynamics. The Hamiltonian function is used to handle the dynamic of agent, while the Casimir function is constructed to deal with the dynamic of link. Thus the Lyapunov function is generated by modifying the Hamiltonian...