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## Grunbaum coloring and its generalization to arbitrary dimension

Australasian Journal of Combinatorics. 2017. Vol. 67. No. 2. P. 119-130.

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.

Publication based on the results of:

Shabanov D. A., European Journal of Combinatorics 2015 Vol. 43 P. 185-203

An equitable two-coloring of a hypergraph $H=(V,E)$ is a proper vertex two-coloring such that the cardinalities of color classes differ by at most one. In connection with the property B problem Radhakrishnan and Srinivasan proved that if $H$ is a $k$-uniform hypergraph with maximum vertex degree $\Delta(H)$ satisfying
$$
\Delta(H)\leqslant c\,\frac {2^{k-1}}{\sqrt{k\,\ln k}}
$$
for some absolute constant ...

Added: October 6, 2015

Pham S. K., Antipov D., Sirotkin Alexander et al., Journal of Computational Biology 2013 Vol. 20 No. 4 P. 359-371

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 ...

Added: March 21, 2014

Shabanov D. A., Graphs and Combinatorics 2014 Vol. 30 No. 5 P. 1249-1260

The work deals with a generalization of Erdos-Lovasz problem concerning colorings of non-uniform hypergraphs. We establish a new sufficient condition for r-colorability of a non-unifrom hypergraph with large edge sizes and girth at leats 4 in terms of expectation of the number of monochromatic edges in a random coloring. ...

Added: December 15, 2015

Berlin : Springer, 2014

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

Added: June 7, 2014

Kokhov V. A., Ткаченко С. В., Программные продукты и системы 2010 № 4 С. 22-22

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. ...

Added: October 14, 2012

Shabanov D. A., Kozik J., Journal of Combinatorial Theory. Series B 2016 Vol. 116 P. 312-332

The paper deals with extremal problems concerning colorings of hypergraphs. By using a random recoloring algorithm we show that any n-uniform simple (i.e. every two distinct edges share at most one vertex) hypergraph H with not large maximum edge degree is r-colorable. As an application of our proof technique we establish a new lower bound ...

Added: December 15, 2015

Danilov V., Rakhel M., Russian Journal of Mathematical Physics 2021 Vol. 28 No. 2 P. 179-187

In this paper, we show how to construct an asymptotic representation of the fundamental solution to the Cauchy problem for degenerate linear parabolic equations. ...

Added: June 6, 2021

Akopov A. S., Beklaryan L. A., Saghatelyan A. K., Environmental Modelling and Software 2019 Vol. 116 P. 7-25

Urban greenery such as trees can effectively reduce air pollution in a natural and eco-friendly way. However, how to spatially locate and arrange greenery in an optimal way remains as a challenging task. We developed an agent-based model of air pollution dynamics to support the optimal allocation and configuration of tree clusters in a city. The Pareto ...

Added: February 24, 2019

Lanham : University Press of America, 2012

The history of logic and analytic philosophy in Central and Eastern Europe is still known to very few people. As an exception to the rule, only two scientific schools became internationally popular: the Vienna Circle and the Lvov-Warsaw School. Nevertheless, the countries included in this region have not only joint history, but also joint cultural ...

Added: February 13, 2013

Malyshev D., Discrete Mathematics 2015 Vol. 338 No. 11 P. 1860-1865

We completely determine the complexity status of the 3-colorability problem for hereditary graph classes defined by two forbidden induced subgraphs with at most five vertices. ...

Added: April 7, 2014

Decrouez G. G., Hall P., Bernoulli: a journal of mathematical statistics and probability 2013 Vol. 19 No. 4 P. 1268-1293

Motivated by a problem arising when analysing data from quarantine searches, we explore properties of distributions of sums of independent means of independent lattice-valued random variables. The aim is to determine the extent to which approximations to those sums require continuity corrections. We show that, in cases where there are only two different means, the ...

Added: September 29, 2014

P. : Université Paris 13 - Paris Sorbonne Cité, 2013

In this workshop we will bring together participants who have solutions for one or more of the following problems: How can mutual understanding be optimized with the help of technology in hospitals where both patients and professionals have varying language skills, cultural backgrounds and cognitive capacities? Can domain ontologies, natural language processing tools, multilingual knowledge-based ...

Added: December 18, 2014

Malyshev D., Alekseev V., Дискретный анализ и исследование операций 2008 Т. 15 № 1 С. 3-10

Доказывается полиномиальная разрешимость задачи о независимом множестве для бесконечного семейства подмножеств класса планарных графов. ...

Added: August 31, 2012

Malyshev D., Journal of Applied and Industrial Mathematics 2020 Vol. 14 No. 4 P. 706-721

The edge coloring problem for a graph is to minimize the number of colors that are sufficient to color all edges of the graph so that all adjacent edges receive distinct colors. The computational complexity of the problem is known for all graph classes defined by forbidden subgraphs with at most 6 edges. We improve ...

Added: January 30, 2021

Nicol R., Chapman S., Vertes P. et al., Journal of Neurophysiology (США) 2012 Vol. 107 No. 5 P. 1421-1430

How do human brain networks react to dynamic changes in the sensory environment? We measured rapid changes in brain network organization in response to brief, discrete, salient auditory stimuli. We estimated network topology and distance parameters in the immediate central response period, <1 s following auditory presentation of standard tones interspersed with occasional deviant tones ...

Added: October 23, 2014

Николаев М. В., Nikitin A. A., Дифференциальные уравнения 2019 Т. 55 № 9 С. 1209-1217

В работе изучается нелинейное интегральное уравнение, возникающее в результате параметрического замыкания третьего пространственного момента в модели У. Дикмана и Р. Лоу. Исследуется вопрос о существовании неподвижной точки интегрального оператора, задаваемого данным уравнением. Доказывается некомпактность полученного оператора. Формулируются условия, при которых уравнение имеет нетривиальное решение. ...

Added: November 7, 2019

Bliznets Ivan, Cygan M., Komosa P. et al., ACM Transactions on Computation Theory 2018 Vol. 10 No. 2 P. 1-32

The H-free Edge Deletion problem asks, for a given graph G and integer k, whether it is possible to delete at most k edges from G to make it H-free—that is, not containing H as an induced subgraph. The H-free Edge Completion problem is defined similarly, but we add edges instead of deleting them. The study of these two problem families has recently been the subject of intensive studies from the point of ...

Added: October 30, 2018

Beklemishev L. D., Оноприенко А. А., Математический сборник 2015 Т. 206 № 9 С. 3-20

We formulate some term rewriting systems in which the number of computation steps is finite for each output, but this number cannot be bounded by a provably total computable function in Peano arithmetic PA. Thus, the termination of such systems is unprovable in PA. These systems are derived from an independent combinatorial result known as the Worm ...

Added: March 13, 2016

Logvenkov S. A., Штейн А. А., Российский журнал биомеханики 2013 Т. 17 № 4 С. 47-57

The mathematical modelling is performed to study the effect of the permeability of the Casparian bands to water and solutes on the formation of the root pressure. It is shown that the pressure in the xylem vessels which stops the flow across a root cut (root pressure) decreases with increase in the permeability of the ...

Added: January 30, 2014

Skoptsov K. A., Sheshenin S., Galatenko V. V. et al., International Journal of Applied Mechanics 2016 Vol. 8 No. 2 P. 1650016-01-1650016-18

We present a method for evaluating elastic properties of a composite material produced by molding a resin filled with short elastic fibers. A flow of the filled resin is simulated numerically using a mesh-free method. After that, assuming that spatial distribution and orientation of fibers are not significantly changed during polymerization, effective elastic moduli of ...

Added: May 22, 2016

Decrouez G. G., Robinson A., Risk Analysis: An International Journal 2013 Vol. 33 No. 12 P. 2142-2153

We propose a new modeling approach for inspection data that provides a more useful interpretation of the patterns of detections of invasive pests, using cargo inspection as a motivating example. Methods that are currently in use generally classify shipments according to their likelihood of carrying biosecurity risk material, given available historical and contextual data. Ideally, ...

Added: September 29, 2014

Chernyshev S. V., Cherepanov E. A., Pankratiev E. V. et al., Journal of Mathematical Sciences 2005 Vol. 128 No. 6 P. 3487-3495

Added: January 27, 2014

Bagrov A. N., Gordin V. A., Bykov P. L., Russian Meteorology and Hydrology 2014 No. 5 P. 283-291

The evaluations of the forecasts of surface air temperature and precipitation for the period July 2010 - June 2013 are presented. The forecasting of surface air temperature at 5 days and precipitation at 3 days are considered. Our complex statistical scheme uses the results of the best foreign global schemes, regional scheme COSMO-RU7. The joint ...

Added: December 7, 2013

Красноярск : ИВМ СО РАН, 2013

Труды Пятой Международной конференции «Системный анализ и информационные технологии» САИТ-2013 (19–25 сентября 2013 г., г.Красноярск, Россия): ...

Added: November 18, 2013