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## Grunbaum coloring and its generalization to arbitrary dimension

This paper is a collection of thoughts and observations, being partly a review and partly a report of current research, on recent work in various aspects of Grunbaum colorings, their existence and usage. In particular, one of the most striking significances of Grunbaum’s Conjecture in the 2-dimensional case is its equivalence to the 4-Color Theorem. The notion of Grunbaum coloring is extended from the 2-dimensional case to the case of arbitrary finite hyper-dimensions.

This paper describes our approach to document search based on the ontological resources and graph models. The approach is applicable in local networks and local computers. It can be useful for ontology engineering specialists or search specialists.

*The article describes the original software tools for an experimental estimation of computational complexity of software solutions for problems on graph models of systems. The classes of the solved problems and the tools for analysis of results are listed. The method based on selection of graph models by their structural complexity is introduced.*

One of the key advances in genome assembly that has led to a significant improvement in contig lengths has been improved algorithms for utilization of paired reads (mate-pairs). While in most assemblers, mate-pair information is used in a post-processing step, the recently proposed Paired de Bruijn Graph (PDBG) approach incorporates the mate-pair information directly in the assembly graph structure. However, the PDBG approach faces difficulties when the variation in the insert sizes is high. To address this problem, we first transform mate-pairs into edge-pair histograms that allow one to better estimate the distance between edges in the assembly graph that represent regions linked by multiple mate-pairs. Further, we combine the ideas of mate-pair transformation and PDBGs to construct new data structures for genome assembly: pathsets and pathset graphs.

The paper deals with the classical extremal problem concerning colorings of hypergraphs. The problem is to find the value m(n,r), equal to the minimum number of edges in a n-uniform hypergraph with chromatic number greater than r. We obtain new upper and lower bounds for m(n,r) in the case when the parameter r is very large in comparison with n.

The book contains the necessary information from the algorithm theory, graph theory, combinatorics. It is considered partially recursive functions, Turing machines, some versions of the algorithms (associative calculus, the system of substitutions, grammars, Post's productions, Marcov's normal algorithms, operator algorithms). The main types of graphs are described (multigraphs, pseudographs, Eulerian graphs, Hamiltonian graphs, trees, bipartite graphs, matchings, Petri nets, planar graphs, transport nets). Some algorithms often used in practice on graphs are given. It is considered classical combinatorial configurations and their generating functions, recurrent sequences. It is put in a basis of the book long-term experience of teaching by authors the discipline «Discrete mathematics» at the business informatics faculty, at the computer science faculty* *of National Research University Higher School of Economics, and at the automatics and computer technique faculty of National research university Moscow power engineering institute. The book is intended for the students of a bachelor degree, trained at the computer science faculties in the directions 09.03.01 Informatics and computational technique, 09.03.02 Informational systems and technologies, 09.03.03 Applied informatics, 09.03.04 Software Engineering, and also for IT experts and developers of software products.

In this paper we present some preliminary results for text corpus visualization by means of so-called reference graphs. The nodes of this graph stand for key words or phrases extracted from the texts and the edges represent the reference relation. The node A refers to the node B if the corresponding key word / phrase B is more likely to co-occur with key word / phrase A than to occur on its own. Since reference graphs are directed graphs, we are able to use graphtheoretic algorithms for further analysis of the text corpus. The visualization technique is tested on our own Web-based corpus of Russian-language newspapers.

The article focuses on the Bluetooth Low Energy technology and the organization of indoor navigation and identification in the buildings by using portable beacons. College campuses, large office buildings, airport terminals, hospitals and other objects are considered to be the possible sphere of usage of such technology. The main purpose of this project is to help people to navigate in such buildings via software and mobile devices.

Graph Structures for Knowledge Representation and Reasoning 2014. Workshop on IJCAI-2014.

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.