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Closure for the property of having a hamiltonian prism

2007
*
Journal of Graph Theory
*

In particular, this problem asks whether

doi:10.1002/jgt.20203
fatcat:jbv6hlpa7jgt5latwibva4gv3m
*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). ...##
###
Hamilton cycles in prisms

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*. ...

##
###
Combinatorial manifolds are Hamiltonian
[article]

2018
*
arXiv
*
pre-print

Extending

arXiv:1806.06436v1
fatcat:nzxrxw75qfbyvb63plhosw3n3q
*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. ...##
###
A "Helium atom" of space: Dynamical instability of the isochoric pentahedron

2013
*
Physical Review D
*

We present an analysis

doi:10.1103/physrevd.87.044047
fatcat:q5rqdi4eubdlray5v5cx6lbrui
*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 . ...##
###
Structure of binary polymer blends: Multiple time step hybrid Monte Carlo simulations and self‐consistent integral‐equation theory

1995
*
Journal of Chemical Physics
*

We examine both

doi:10.1063/1.470189
fatcat:rqzbun6dezcf7ejhaibkduk3ua
*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. ...##
###
Self-consistent integral equation theory for solutions of finite extensible semiflexible polyelectrolyte chains

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 ͒ ...

##
###
On graph closures

2003
*
Discrete Mathematics
*

Theory B 70 (1997) 217) introduced

doi:10.1016/s0012-365x(02)00573-3
fatcat:ygeq3yojdvanfcy6b4tohflvby
*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. ...##
###
Hamiltonian evolutionary games

2015
*
Journal of Dynamics & Games
*

We also introduce

doi:10.3934/jdg.2015.2.33
fatcat:rjztqgysvfbvnm2wtgkbzhjnly
*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 ...##
###
Barbero-Immirzi parameter in Regge calculus
[article]

2008
*
arXiv
*
pre-print

variables plus topological (on equations

arXiv:0804.2389v2
fatcat:hjkj6ttjuzgjjldimef2wafdqi
*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. ...##
###
Thermodynamic properties of freely-jointed hard-sphere multi-Yukawa chain fluids: theory and simulation

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. ...

##
###
Electron propagation in orientationally disordered fullerides

1994
*
Physical Review B (Condensed Matter)
*

, and

doi:10.1103/physrevb.50.2150
pmid:9976428
fatcat:gqygyuuvybgl5ihmhtxdrbsqvi
*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] . ...##
###
On positivity of quantum measure and of effective action in area tensor Regge calculus
[article]

2007
*
arXiv
*
pre-print

We speculate that positivity

arXiv:0707.3331v1
fatcat:i5pd6asq4rdkrnanrllhxzh2my
*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. ...##
###
Network Hamiltonian models reveal pathways to amyloid fibril formation

2020
*
Scientific Reports
*

This paper introduces

doi:10.1038/s41598-020-72260-8
pmid:32973286
pmcid:PMC7515878
fatcat:r3awd3llsjcwrk5tn7xvnejpxe
*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. ...##
###
Decomposing infinite matroids into their 3-connected minors

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. ...

##
###
Faithful subgraphs and Hamiltonian circles of infinite graphs
[article]

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. ...

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