On the Konig graphs for the 5-path and its spanning supergraphs
We describe the hereditary class of graphs, whose every subgraph has the property that the maximum number of disjoint 5-paths (paths on 5 vertices) is equal to the minimum size of the sets of vertices having nonempty intersection with the vertex set of each 5-path. We describe this class in terms of the "forbidden subgraphs" and give an alternative description, using some operations on pseudographs.
We characterize the graphs whose each induced subgraph has the property: the packing number of induced 3-paths is equal to the corresponding vertex cover number.
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.
We describe the class of graphs whose each subgraph has the next property: The maximal number of disjoint 4-paths is equal to the minimal cardinality of sets of vertices such that every 4-path in the subgraph contains at least one of these vertices. We completely describe the set of minimal forbidden subgraphs for this class. Moreover, we present an alternative description of the class based on the operations of edge subdivision applied to bipartite multigraphs and the addition of so-called pendant subgraphs, isomorphic to triangles and stars.
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.