On the theory of the simplest extremal systems of self-oscillatory type

1967 ◽  
Vol 10 (3) ◽  
pp. 210-216
Author(s):  
N. N. Leonov
Keyword(s):  
Extremal Systems

scholarly journals Shattering, Graph Orientations, and Connectivity

10.37236/3326 ◽  
2013 ◽  
Vol 20 (3) ◽  
Author(s):  
László Kozma ◽  
Shay Moran
Keyword(s):  
Graph Theory ◽  
Combinatorial Optimization ◽  
Main Tool ◽  
The Other ◽  
Vc Dimension ◽  
Forbidden Subgraphs ◽  
Set Systems ◽  
Flows In Networks ◽  
Extremal Systems

We present a connection between two seemingly disparate fields: VC-theory and graph theory. This connection yields natural correspondences between fundamental concepts in VC-theory, such as shattering and VC-dimension, and well-studied concepts of graph theory related to connectivity, combinatorial optimization, forbidden subgraphs, and others.In one direction, we use this connection to derive results in graph theory. Our main tool is a generalization of the Sauer-Shelah Lemma (Pajor, 1985; Bollobás and Radcliffe, 1995; Dress, 1997; Holzman and Aharoni). Using this tool we obtain a series of inequalities and equalities related to properties of orientations of a graph. Some of these results appear to be new, for others we give new and simple proofs.In the other direction, we present new illustrative examples of shattering-extremal systems - a class of set-systems in VC-theory whose understanding is considered by some authors to be incomplete Bollobás and Radcliffe, 1995; Greco, 1998; Rónyai and Mészáros, 2011). These examples are derived from properties of orientations related to distances and flows in networks.

Optimal control in extremal systems

1971 ◽  
Vol 14 (3) ◽  
pp. 304-307
Author(s):  
N. N. Leonov
Keyword(s):  
Optimal Control ◽  
Extremal Systems

Certain algorithms for sequential storage in extremal systems

1972 ◽  
Vol 15 (11) ◽  
pp. 1334-1343
Author(s):  
V. N. Smirnova ◽  
M. L. Tai
Keyword(s):  
Extremal Systems

Extremal systems with dominant search

1971 ◽  
Vol 14 (3) ◽  
pp. 295-303
Author(s):  
N. N. Leonov
Keyword(s):  
Extremal Systems

Correlated-Extremal Systems and Sensors

2016 ◽  
pp. 179-201
Author(s):  
Evgeny A. Konovalov ◽  
Sergey P. Faleev
Keyword(s):  
Extremal Systems
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