Edge disjoint realization problems have connections for example to discrete tomography. In this paper, we consider the edge caterpillar realizations of tree degree sequences. We give necessary and sufficient conditions when two sequences realizations. conjecture that an arbitrary number if every vertex is a leaf in at most one tree. prove true four. also n ≥ max { 22 k − 11 , 396 } where vertices

The paper describes the change of geometry caterpillar terrestrial robotic complex depending on external factors. It is established that as a result action centrifugal forces elongates, surface support rollers, repeats their shape, upper part acquires convex and lower shape curve, which determines unevenness soil. dependence soil irregularities established. peculiarity there ripple with number ...

In the first part of this paper we present the first steps towards providing low-risk and economically feasible network data transfer services. We introduce three types of data transfer services and present general guidelines and algorithms for managing service prices, risks and schedules. In the second part of the paper we solve two packet scheduling cost optimization problems and present effi...

A graceful labeling of a graph G of size n is an injective assignment of integers from {0, 1,..., n} to the vertices of G, such that when each edge of G has assigned a weight, given by the absolute dierence of the labels of its end vertices, the set of weights is {1, 2,..., n}. If a graceful labeling f of a bipartite graph G assigns the smaller labels to one of the two stable sets of G, then f ...

Nowadays, it is a common practice to protect various types of statistical data before publishing them for different researches. For instance, when conducting extensive demographic surveys such as national census, the collected data should be at least depersonalized to guarantee proper level of privacy preservation. In practice, even more complicated methods of data protection need to be used. A...