?
Coloring non-uniform hypergraphs without short cycles
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.
Research target:
Mathematics
Language:
English
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
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
Shabanov D. A., Akhmejanova M., Discrete Mathematics 2020 Vol. 343 No. 4 P. 1-11
The paper deals with an extremal problem concerning colorings of hypergraphs with bounded edge degrees. Consider the family of b-simple hypergraphs, in which any two edges do not share more than b common vertices. We prove a new lower bound for the maximum edge degree in a n-uniform b-simple non-r-colorable hypergraph. We also establish some ...
Added: October 31, 2019
Shabanov D. A., Discrete Mathematics 2015 Vol. 338 No. 11 P. 1976-1981
The work deals with combinatorial problems concerning colorings of non-uniform hypergraphs. Let $H=(V,E)$ be a hypergraph with minimum edge-cardinality $n$. We show that if $H$ is a simple hypergraph (i.e. every two distinct edges have at most one common vertex) and
$$
\sum_{e\in E}r^{1-|e|}\leqslant c\sqrt{n},
$$
for some absolute constant $c>0$, then $H$ is $r$-colorable. We also obtain ...
Added: October 6, 2015
Kravtsov D., Krokhmal N., Shabanov D. A., Russian Mathematical Surveys 2018 Vol. 73 No. 4 P. 731-733
The paper deals with the problem of finding the probability threshold for the
existence of a panchromatic colouring for a random hypergraph in the binomial
model. ...
Added: November 15, 2018
Shabanov D. A., Discrete Applied Mathematics 2020 Vol. 282 P. 168-183
The paper deals with estimating the r-colorability threshold for a random k-uniform hypergraph in the binomial model H(n,k,p). We consider the sparse case, when the expected number of edges is a linear function of n and prove a new lower bound for the sharp threshold of the property that H(n,k,p) is r-colorable. ...
Added: June 6, 2020
Akhmejanova M., Shabanov D. A., Discrete Applied Mathematics 2020 Vol. 276 P. 2-12
The paper deals with an extremal problem concerning equitable colorings of uniform hypergraphs. Recall that a vertex coloring of a hypergraph is called proper if there are no monochromatic edges under this coloring. A hypergraph is said to be equitably r-colorable if there is a proper coloring with r colors such that the sizes of ...
Added: October 31, 2019
Shabanov D. A., Akolzin I., Discrete Mathematics 2016 Vol. 339 No. 12 P. 3020-3031
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 ...
Added: September 4, 2016
Lebedeva A., Фундаментальная и прикладная математика 2014 Т. 19 № 2 С. 125-149
This paper deals with an extremal problem concerning hypergraph colorings. Let k be an integer. The problem is to find the value m(k,n) equal to the minimum number of edges in an n-uniform hypergraph not admitting two-colorings of the vertex set such that every edge of the hypergraph contains at least k vertices of each ...
Added: July 19, 2015
Shabanov D. A., Doklady Mathematics 2017 Vol. 96 No. 1 P. 321-325
The problem on the limit distribution of the chromatic number of a random uniform hypergraph in the sparse case is studied. It is shown that, for most parameters values, the limit distribution of the chromatic number is concentrated at precisely one point, which can be found explicitly. ...
Added: March 6, 2018
Popkov Y., Popkov A., Dubnov Y. A., Автоматика и телемеханика 2020 № 7 С. 148-172
A randomized forecasting method based on the generation of ensembles of entropy-optimal forecasting trajectories is developed. The latter are generated by randomized dynamic regression models containing random parameters, measurement noises, and a random input. The probability density functions of random parameters and measurement noises are estimated using real data within the randomized machine learning procedure. ...
Added: October 31, 2020
Malyshev D., Вестник Нижегородского университета им. Н.И. Лобачевского 2008 № 6 С. 141-146
Рассматривается понятие граничного класса, которое является полезным инструментом для анализа вычислительной сложности задач на графах. Исследуются два конкретных класса графов, и приводятся задачи, для которых эти классы являются граничными. ...
Added: August 31, 2012
Belomestny D., Iosipoi L., Mathematics and Computers in Simulation 2021 No. 181 P. 351-363
Markov Chain Monte Carlo methods become increasingly popular in applied mathematics as a tool for numerical integration with respect to complex and high-dimensional distributions. However, application of MCMC methods to heavy-tailed distributions and distributions with analytically intractable densities turns out to be rather problematic. In this paper, we propose a novel approach towards the use ...
Added: October 31, 2020
Revenko A., Kuznetsov S., Fundamenta Informaticae 2012 Vol. 4 No. 115 P. 377-394
An approach for studying relations between properties of functions on sets is proposed. The approach is based on Attribute Exploration. 16 properties of functions are considered, among them monotonicity, idempotency, path independence, exchange properties, convexity, etc. Example functions are partially computer generated on the powersets of sets with 2, 3 and 4 elements. Attribute Exploration ...
Added: December 31, 2012
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
D. V. Gribanov, D.S. Malyshev, P. M. Pardalos et al., Journal of Combinatorial Optimization 2018 Vol. 35 No. 4 P. 1128-1146
In this paper, we present fixed-parameter tractable algorithms for special cases of the shortest lattice vector, integer linear programming, and simplex width computation problems, when matrices included in the problems’ formulations are near square. The parameter is the maximum absolute value of the rank minors in the corresponding matrices. Additionally, we present fixed-parameter tractable algorithms ...
Added: February 19, 2018
Kryuchkov M., Rusakov S. V., Вестник Ижевского государственного технического университета 2015 № 2(66) С. 110-112
This paper describes the results of testing the neuronal technical trend indicator according to the exchange rate of Brent oil in 2014. Testing of the model was carried out on three time series, which characterized by their features. ...
Added: August 31, 2015
Malyshev D., Дискретный анализ и исследование операций 2012 Т. 19 № 4 С. 66-72
Рассматривается конструктивный подход к формированию новых случаев эффективной разрешимости задачи о независимом множестве в семействе наследственных частей множества графов Free({P5,C5}). Именно, доказывается, что если эта задача полиномиально разрешима в классе Free({P5,C5,G}), то для любого графа H, который может быть индуктивно получен из G применением к текущему графу сложения с K1 или умножения на K1, эта ...
Added: August 31, 2012
Sirotkin D., Malyshev D., Дискретная математика 2017 Т. 29 № 3 С. 114-125
Задача о независимом множестве для заданного обыкновенного графа состоит в вычислении размера наибольшего множества его попарно несмежных вершин. Предлагается новый способ редукции графов. С его помощью получено новое доказательство NP-полноты задачи о независимом множестве в классе планарных графов и доказана NP-полнота данной задачи в классе плоских графов, имеющих только треугольные внутренние грани, с максимальной степенью ...
Added: September 7, 2017
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
Feigin B. L., Finkelberg M. V., Rybnikov L. G. et al., Selecta Mathematica, New Series 2011 Vol. 17 No. 3 P. 573-607
Laumon moduli spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety of GLn. We construct the action of the Yangian of sln in the cohomology of Laumon spaces by certain natural correspondences. We construct the action of the affine Yangian (two-parametric deformation of the universal ...
Added: October 9, 2012
Babash A. V., М. : ИНФРА-М, РИОР, 2013
Пособие предназначено для студентов высших учебных заведений, обучающихся по специальности «Прикладная информатика (в экономике)». Оно также содержит методический материал для ряда инновационных курсов лекций по профилю «Информационная безопасность» и может быть использовано и для блока дисциплин этого профиля. Ряд представленных результатов полезен специалистам и аспирантам, специализирующихся в указанной области. ...
Added: January 14, 2014
Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45
Added: October 17, 2014
Barcelona : IEEE, 2017
International Conference on Control, Decision and Information Technologies. ...
Added: January 17, 2018