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Equivalences between hamiltonicity and flow conjectures, and the sublinear defect property

Martin Kochol
2002 Discrete Mathematics  
We show that many conjectures and theorems about graphs could be proved if one could show that they are true apart from some "errors", provided that the number of these errors grows asymptotically slower  ...  than the order of these graphs.  ...  Acknowledgements This paper was written during the Alexander von Humboldt Fellowship in Germany. The author thanks AvH, Freie University and Professor Aigner for the hospitality.  ... 
doi:10.1016/s0012-365x(01)00372-7 fatcat:ku4scjy3jzawnfqoybuyf3frqa

Page 1602 of Mathematical Reviews Vol. , Issue 2003C [page]

2003 Mathematical Reviews  
Brian Alspach (3-RGN; Regina, SK) 2003¢:05140 05C45 05C38 Kochol, Martin (SK-AOS; Bratislava) Equivalences between Hamiltonicity and flow conjectures, and the sublinear defect property.  ...  Summary: “Barnette’s conjecture (BC) states that every 3- connected cubic bipartite planar graph admits a Hamilton cycle. It is shown that BC is equivalent to a conjecture stated in this pa- per.  ... 

How Many Conjectures Can You Stand? A Survey

H. J. Broersma, Z. Ryjáček, P. Vrána
2011 Graphs and Combinatorics  
These conjectures have lead to a wealth of interesting concepts, techniques, results and equivalent conjectures.  ...  We survey results and open problems in hamiltonian graph theory centered around two conjectures of the 1980s that are still open: every 4-connected claw-free graph (line graph) is hamiltonian.  ...  Kochol [40] proved equivalence with seemingly weaker versions, using a concept called sublinear defect. As an example, he proved that Conjecture 2 is equivalent to the following conjecture.  ... 
doi:10.1007/s00373-011-1090-6 fatcat:jj7oxvyx5vhrzdjtv2qyj7nysy

Algorithm for Overcoming the Curse of Dimensionality for State-dependent Hamilton-Jacobi equations [article]

Yat Tin Chow, Jerome Darbon, Stanley Osher, Wotao Yin
2018 arXiv   pre-print
In this paper, we develop algorithms to overcome the curse of dimensionality in possibly non-convex state-dependent Hamilton-Jacobi equations (HJ PDEs) arising from optimal control and differential game  ...  We extend [5, 6, 8], and conjecture a (Lax-type) minimization principle when the Hamiltonian is convex, as well as a (Hopf-type) maximization principle when the Hamiltonian is non-convex.  ...  Wilfrid Gangbo for exploring if the conjectures made in this paper are sound. We also thank Alex Tong Lin for many discussions of insights in our paper.  ... 
arXiv:1704.02524v3 fatcat:4kcoklehknelfccu37ixsywwpm

Page 172 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
(English summary) 2003f:05078 Kochol, Martin Equivalences between Hamiltonicity and flow conjectures, and the sublinear defect property. (English summary) 2003c:05140 Kostochka, A.  ...  (English summary) — (with Ong, Siew-Hui) On Barnette’s conjecture and CBP graphs with given number of Hamilton cycles.  ... 

Linear growth of the entanglement entropy and the Kolmogorov-Sinai rate

Eugenio Bianchi, Lucas Hackl, Nelson Yokomizo
2018 Journal of High Energy Physics  
Finally, we conjecture that the same rate Λ_A appears in the entanglement growth of chaotic quantum systems prepared in a semiclassical state.  ...  We show that the entanglement entropy S_A of a Gaussian state grows linearly for large times in unstable systems, with a rate Λ_A ≤ h_KS determined by the Lyapunov exponents and the choice of the subsystem  ...  The second term measures energy flow between the subsystem A and its complement, as measured by the effective Hamilto-nianH A of the subsystem defined in eq. (7.5).  ... 
doi:10.1007/jhep03(2018)025 fatcat:vyolxhc3m5ejznqtvseeogchqq

Subject Index Volumes 1–200

2001 Discrete Mathematics  
Erdös and Sós, 4925 Erdös and Szekeres, 4879 Erdös et al., 5529, 5888 Erdös Rubin Taylor, 3815 Erdös Sós Turán, 506 Everett, 2901 Faigle and Sands, 2122 Faudree et al., 4399 Faudree Gould Jacobson  ...  Slater, 5299 Hertz and de Werra, 3748 Hibi, 4839 Hoàng, 3748, 4811 Holton, 1660 Holyer and Cockayne, 1118 Howorka, 2636  ...  , see also Hamiltonian and Hamiltonicity Hamiltonian, 51, 146, 205, 250, 442, 447, 477, 527, 603, 708, 805, 1106 , 1132 , 1133 , 1141 , 1207 , 1302 , 1398 , 1417 , 1524 , 1525 , 1639 , 1752 , 1971 , 2067  ... 
doi:10.1016/s0012-365x(00)00471-4 fatcat:znxg54q6ifgutnhzj3urcw455y

Twentieth Annual Meeting February 24–27, 1976 Olympic Hotel, Seattle, Washington

1976 Biophysical Journal  
In contrast, rabbit troponin increases the Ca2+-sensitivity of the scallop fibers ten-fold such that the relationship between % Ca2+-activated tension and % Ca2+ binding to troponin is the same for identical  ...  The frictional coefficient measured by these techniques was compared to the calculated value for an equivalent hydrated sphere of the same molecular weight. The data of I. D.  ...  .), and both of the above conjectures were confirmed.  ... 
doi:10.1016/s0006-3495(76)85676-7 fatcat:q2qfvlueibahpdvcbyuwef3ygm

Mathematical and Algorithmic Analysis of Network and Biological Data [article]

Charalampos E. Tsourakakis
2014 arXiv   pre-print
This dissertation contributes to mathematical and algorithmic problems that arise in the analysis of network and biological data.  ...  Equivalently, the effective resistance is the potential difference that appears across terminals i and j when we apply a unit current source between them.  ...  Main Program Flow: The main flow comprises iterative execution of SQL statements with appropriate user defined functions.  ... 
arXiv:1407.0375v1 fatcat:6s2qka5fazbl7bzxz4k3u75hzm

A framework for three-dimensional navigation research

Kathryn J. Jeffery, Aleksandar Jovalekic, Madeleine Verriotis, Robin Hayman
2013 Behavioral and Brain Sciences  
Three broad categories organize the experimental and theoretical issues raised by the commentators: (1) frames of reference, (2) comparative cognition, and (3) the role of experience.  ...  AbstractWe have argued that the neurocognitive representation of large-scale, navigable three-dimensional space is anisotropic, having different properties in vertical versus horizontal dimensions.  ...  (G1100669), and the Biotechnology and Biological Sciences Research Council (BB/J009792/1), and by a grant to Axona Ltd from the European Commission's Seventh Framework Programme (SPACEBRAIN).  ... 
doi:10.1017/s0140525x13001556 fatcat:2fw4lfhzirfxxhz2nppwaqstum

Making a stronger case for comparative research to investigate the behavioral and neurological bases of three-dimensional navigation

Daniele Nardi, Verner P. Bingman
2013 Behavioral and Brain Sciences  
This comparative approach may offer unique insights into some of the important questions raised by Jeffery et al.  ...  We propose some hypotheses relating differences in natural history to potential behavioral and neurological adaptations possessed by contrasting bird species.  ...  (G1100669), and the Biotechnology and Biological Sciences Research Council (BB/J009792/1), and by a grant to Axona Ltd from the European Commission's Seventh Framework Programme (SPACEBRAIN).  ... 
doi:10.1017/s0140525x13000472 pmid:24103612 fatcat:y72x5vnckbcihl3ks35sy7wj3u

Map fragmentation in two- and three-dimensional environments

Homare Yamahachi, May-Britt Moser, Edvard I. Moser
2013 Behavioral and Brain Sciences  
How map fragments are linked, which brain circuits are involved, and whether metric is preserved across fragments are questions that remain to be determined.  ...  AbstractThe suggestion that three-dimensional space is represented by a mosaic of neural map fragments, each covering a small area of space in the plane of locomotion, receives support from studies in  ...  (G1100669), and the Biotechnology and Biological Sciences Research Council (BB/J009792/1), and by a grant to Axona Ltd from the European Commission's Seventh Framework Programme (SPACEBRAIN).  ... 
doi:10.1017/s0140525x13000605 pmid:24103625 fatcat:yizukbxq7zezhnidhlaobldn6q

Navigating in a Three-Dimensional World [chapter]

Kathryn J. Jeffery
2011 Animal Thinking  
The present article reviews the emerging behavioral and neurobiological literature on spatial cognition in non-horizontal environments.  ...  However, the real world is three-dimensional, having a complex topography including both horizontal and vertical features, which presents additional challenges for representation and navigation.  ...  (G1100669), and the Biotechnology and Biological Sciences Research Council (BB/J009792/1), and by a grant to Axona Ltd from the European Commission's Seventh Framework Programme (SPACEBRAIN).  ... 
doi:10.7551/mitpress/9780262016636.003.0003 fatcat:6dlac5a63nhhth776y5scyluwa

Think local, act global: How do fragmented representations of space allow seamless navigation?

Paul A. Dudchenko, Emma R. Wood, Roderick M. Grieves
2013 Behavioral and Brain Sciences  
AbstractIn this commentary, we highlight a difficulty for metric navigation arising from recent data with grid and place cells: the integration of piecemeal representations of space in environments with  ...  One implication of this is that the capacity for spatial inferences may be limited.  ...  (G1100669), and the Biotechnology and Biological Sciences Research Council (BB/J009792/1), and by a grant to Axona Ltd from the European Commission's Seventh Framework Programme (SPACEBRAIN).  ... 
doi:10.1017/s0140525x13000368 pmid:24103601 fatcat:sbioi44ngbavbk26znoqx7kvjy

Navigating in a three-dimensional world

Kathryn J. Jeffery, Aleksandar Jovalekic, Madeleine Verriotis, Robin Hayman
2013 Behavioral and Brain Sciences  
The present article reviews the emerging behavioral and neurobiological literature on spatial cognition in non-horizontal environments.  ...  However, the real world is three-dimensional, having a complex topography including both horizontal and vertical features, which presents additional challenges for representation and navigation.  ...  (G1100669), and the Biotechnology and Biological Sciences Research Council (BB/J009792/1), and by a grant to Axona Ltd from the European Commission's Seventh Framework Programme (SPACEBRAIN).  ... 
doi:10.1017/s0140525x12002476 pmid:24103594 fatcat:z6wa67wr3jar3m2p2b6qf6g3zm
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