Article
Некоторые результаты о наследственных классах графов III
For a graph property X, let Xn be the number of graphs with vertex set {1, . . . , n} having property X, also known as the speed of X. A property X is called factorial if X is hereditary (i.e. closed under taking induced subgraphs) and nc1n ≤ Xn ≤ nc2n for some constants c1 and c2. Hereditary properties with speed slower than factorial are surprisingly well structured. The situation with factorial properties is more complicated and less explored. Only the properties with speeds up to the Bell number are well studied and well behaved. To better understand the behavior of factorial properties with faster speeds we introduce a structural tool called locally bounded coverings and show that a variety of graph properties can be described by means of this tool.
For a graph property X, let Xn be the set of graphs with the vertex set {1, . . . , n} that satisfy the property X. A property X is called factorial if X is hereditary (i. e. closed under taking induced subgraphs) and nc1n ≤ X ≤ nc2n for some positive constants c1 and c2. A graph G is a quasi-line if for every vertex v, the set of neighbors of v can be expressed as a union of two cliques. In the present paper we identify almost all factorial subclasses of quasi-line graphs defined by one forbidden induced subgraph. We use these new results to prove that the class Free(K1,3,W4) is factorial, which improves on a result of Lozin, Mayhill and Zamaraev [8].
The Independent Set Problem for planar graphs is known to be NP-complete. In this paper, its polynomial solvability for some subclasses of planar graphs is proved.
This proceedings publication is a compilation of selected contributions from the “Third International Conference on the Dynamics of Information Systems” which took place at the University of Florida, Gainesville, February 16–18, 2011. The purpose of this conference was to bring together scientists and engineers from industry, government, and academia in order to exchange new discoveries and results in a broad range of topics relevant to the theory and practice of dynamics of information systems. Dynamics of Information Systems: Mathematical Foundation presents state-of-the art research and is intended for graduate students and researchers interested in some of the most recent discoveries in information theory and dynamical systems. Scientists in other disciplines may also benefit from the applications of new developments to their own area of study.
When a society needs to take a collective decision one could apply some aggregation method, particularly, voting. One of the main problems with voting is manipulation. We say a voting rule is vulnerable to manipulation if there exists at least one voter who can achieve a better voting result by misrepresenting his or her preferences. The popular approach to comparing manipulability of voting rules is defining complexity class of the corresponding manipulation problem. This paper provides a survey into manipulation complexity literature considering variety of problems with different assumptions and restrictions.
A form for an unbiased estimate of the coefficient of determination of a linear regression model is obtained. It is calculated by using a sample from a multivariate normal distribution. This estimate is proposed as an alternative criterion for a choice of regression factors.