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Closure for the property of having a hamiltonian prism

Daniel Král, Ladislav Stacho
2007 Journal of Graph Theory  
In particular, this problem asks whether the property of "having a hamiltonian prism" is n-stable for graphs of order n.  ...  In this paper, we answer this problem in negative by constructing graphs that show the property of "having a hamiltonian prism" is not k-stable for k = 4n/3 − 16/3 (Proposition 1).  ... 
doi:10.1002/jgt.20203 fatcat:jbv6hlpa7jgt5latwibva4gv3m

Hamilton cycles in prisms

Tomáš Kaiser, Zdeněk Ryjáček, Daniel Král, Moshe Rosenfeld, Heinz-Jürgen Voss
2007 Journal of Graph Theory  
The property of having a hamiltonian prism is 'sandwiched' between the existence of a 2-tree and the existence of a 2-walk: Both implications are sharp.  ...  The central theme of the present paper is a refinement of this hierarchy involving hamilton cycles in the prism G2K 2 over a graph G. If the prism is hamiltonian, we call G prism-hamiltonian.  ...  As for the second implication in (1) , any graph G with a hamiltonian prism has a 2-walk that follows the edges of G corresponding to the edges of the hamilton cycle in the prism.  ... 
doi:10.1002/jgt.20250 fatcat:n26mgurf4ndbtmli6vemm5zey4

Combinatorial manifolds are Hamiltonian [article]

Oliver Knill
2018 arXiv   pre-print
Extending a theorem of Whitney of 1931 we prove that all connected d-graphs are Hamiltonian for positive d.  ...  The proof is constructive and shows that unlike for general graphs, the complexity of the construction of Hamiltonian cycles in d-graphs is polynomial in the number of vertices of the graph.  ...  A Hamiltonian path passing through either a or b, can make a detour of the central point c splitting (a, b) and have the Hamiltonian property for the edge refined complex.  ... 
arXiv:1806.06436v1 fatcat:nzxrxw75qfbyvb63plhosw3n3q

A "Helium atom" of space: Dynamical instability of the isochoric pentahedron

C. E. Coleman-Smith, B. Müller
2013 Physical Review D  
We present an analysis of the dynamics of the equifacial pentahedron on the Kapovich-Millson phase space under a volume preserving Hamiltonian.  ...  The classical dynamics of polyhedra under such a Hamiltonian may arise from the classical limit of the node volume operators in loop quantum gravity.  ...  The canonical momenta have dimensions of area so the Hamiltonian must have dimensions of A 3/2 .  ... 
doi:10.1103/physrevd.87.044047 fatcat:q5rqdi4eubdlray5v5cx6lbrui

Structure of binary polymer blends: Multiple time step hybrid Monte Carlo simulations and self‐consistent integral‐equation theory

Dmitry G. Gromov, Juan J. de Pablo
1995 Journal of Chemical Physics  
We examine both the cases of atomic and molecular closures and consider both conventional and self-consistent PRISM.  ...  A newly developed self-consistent formulation of the polymer reference interaction site model ͑PRISM͒ theory is used to predict the structure of binary polymer blends.  ...  ACKNOWLEDGMENTS The authors are grateful to J. Curro and J. McCoy for sending us a reprint of their work ͑Ref. 9͒ prior to publication.  ... 
doi:10.1063/1.470189 fatcat:rqzbun6dezcf7ejhaibkduk3ua

Self-consistent integral equation theory for solutions of finite extensible semiflexible polyelectrolyte chains

T. Hofmann, R. G. Winkler, P. Reineker
2003 Journal of Chemical Physics  
The bare chain stiffness has a pronounced influence on the conformational and structural properties of the solution.  ...  The conformational properties of the polymer chain are determined from a variational calculation with a semiflexible reference chain.  ...  Various such closure relations have been proposed. 37,58,74 -76 In this work we use the Laria-Wu-Chandler ͑LWC͒ closure which proved to be adequate for threadlike polyelectrolytes and is given by ͑r ͒  ... 
doi:10.1063/1.1557472 fatcat:thgsncrlynenpm3vhkkrucwvta

On graph closures

Alexander Kelmans
2003 Discrete Mathematics  
Theory B 70 (1997) 217) introduced a very useful notion of a closure cl(G) for a claw-free graph G and proved, in particular, that c(G) = c(cl(G)) where c(H ) is the length of a longest cycle in H .  ...  As a byproduct, we give some new su cient conditions for graphs to have a Hamiltonian cycle, path, v-path, and uv-path, and show, in particular, that every claw-free 9-connected graph is Hamiltonian connected  ...  Acknowledgements I am thankful to the referees for a very careful reading of the paper and useful remarks.  ... 
doi:10.1016/s0012-365x(02)00573-3 fatcat:ygeq3yojdvanfcy6b4tohflvby

Hamiltonian evolutionary games

Hassan Najafi Alishah, Pedro Duarte
2015 Journal of Dynamics & Games  
We also introduce a new class of Poisson structures on the phase space of these systems, and characterize the corresponding subclass of Hamiltonian polymatrix replicator systems.  ...  We introduce a class of o.d.e.'s that generalizes to polymatrix games the replicator equations on symmetric and asymmetric games.  ...  The second author was supported by "Fundação para a Ciência e a Tecnologia" through the Program POCI 2010 and the Project "Randomness in Deterministic Dynamical Systems and Applications" (PTDC-MAT-105448  ... 
doi:10.3934/jdg.2015.2.33 fatcat:rjztqgysvfbvnm2wtgkbzhjnly

Barbero-Immirzi parameter in Regge calculus [article]

V.M. Khatsymovsky
2008 arXiv   pre-print
variables plus topological (on equations of motion for connections) term with coefficient 1/γ, γ is Barbero-Immirzi parameter.  ...  We consider Regge calculus in the representation in terms of area tensors and self- and antiselfdual connections generalised to the case of Holst action that is standard Einstein action in the tetrad-connection  ...  As a result, we get simply the closure condition for the surface of Hamiltonian formulation leading to a simple form of the functional integral.  ... 
arXiv:0804.2389v2 fatcat:hjkj6ttjuzgjjldimef2wafdqi

Thermodynamic properties of freely-jointed hard-sphere multi-Yukawa chain fluids: theory and simulation

Clare McCabe, Yurij V. Kalyuzhnyi, Peter T. Cummings
2002 Fluid Phase Equilibria  
The spheres each have a hard core and an attractive interaction, written as a single Yukawa potential or as a sum of Yukawa potentials.  ...  We find that in general the theory performs very well, thus, it provides an analytic route to an equation of state for a well-defined model of chain fluids.  ...  The effort of CMC was supported by the National Science Foundation through Grant CTS-9871919.  ... 
doi:10.1016/s0378-3812(01)00661-6 fatcat:nrs4ckrlxvdjzgqhn75a6sjriq

Electron propagation in orientationally disordered fullerides

E. J. Mele, S. C. Erwin
1994 Physical Review B (Condensed Matter)  
, and a mean free path of approximately 20 Angstroms.  ...  This differs from that previously calculated for the orientationally ordered crystal, but is relatively well described within a disorder-averaged virtual-crystal Hamiltonian, which we derive.  ...  Some of the effects on this disorder on the transport properties and the frequency-dependent conductivity have since been explored [7, 8] .  ... 
doi:10.1103/physrevb.50.2150 pmid:9976428 fatcat:gqygyuuvybgl5ihmhtxdrbsqvi

On positivity of quantum measure and of effective action in area tensor Regge calculus [article]

V. M. Khatsymovsky
2007 arXiv   pre-print
We speculate that positivity of the measure can be expected in the most part of range of variation of area tensors.  ...  Because of unboundedness of the general relativity action, Euclidean version of the path integral in general relativity requires definition.  ...  That is, lateral surfaces of different prisms do not have common triangles.  ... 
arXiv:0707.3331v1 fatcat:i5pd6asq4rdkrnanrllhxzh2my

Network Hamiltonian models reveal pathways to amyloid fibril formation

Yue Yu, Gianmarc Grazioli, Megha H. Unhelkar, Rachel W. Martin, Carter T. Butts
2020 Scientific Reports  
This paper introduces a set of network statistical and topological metrics for quantitative analysis and characterization of the fibrillization mechanisms predicted by the network Hamiltonian model.  ...  A recently introduced topological model for aggregation based on network Hamiltonians is capable of recapitulating the entire process of amyloid fibril formation, beginning with thousands of free monomers  ...  RWM is a CIFAR Fellow.  ... 
doi:10.1038/s41598-020-72260-8 pmid:32973286 pmcid:PMC7515878 fatcat:r3awd3llsjcwrk5tn7xvnejpxe

Decomposing infinite matroids into their 3-connected minors

Elad Aigner-Horev, Reinhard Diestel, Luke Postle
2011 Electronic Notes in Discrete Mathematics  
For a graph property X, let X n be the number of graphs with vertex set {1, . . . , n} having property X, also known as the speed of X.  ...  Faudree and Gould have determined all the forbidden pairs that force the existence of a hamiltonian cycle in a 2-connected graph of sufficiently large order.  ...  We have observed that every nontraceable k-traceable oriented graph contains a hypotraceable oriented graph of order at least k + 1 as induced subdigraph.  ... 
doi:10.1016/j.endm.2011.09.003 fatcat:jje5s3kpgbbqhmvwld3246wgiq

Faithful subgraphs and Hamiltonian circles of infinite graphs [article]

Binlong Li
2019 arXiv   pre-print
For example, we prove that the prism of every 3-connected cubic graph has a Hamiltonian circle, extending the result of the finite case by Paulraja.  ...  A circle of G is Hamiltonian if it meets every vertex (and then every end) of G. In this paper, we study a method for finding Hamiltonian circles of graphs.  ...  Conversely, if a 2-factor F satisfies (1) (2) , then the closure of F is a Hamiltonian circle of G.  ... 
arXiv:1902.06402v2 fatcat:5bqhsjz7afgsvibqe4lyyitbmm
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