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Diskretnaya Matematika, 2019, Volume 31, Issue 2, Pages 84–113
DOI: https://doi.org/10.4213/dm1504
(Mi dm1504)
 

This article is cited in 4 scientific papers (total in 4 papers)

Panchromatic colorings of random hypergraphs

D. A. Kravtsova, N. E. Krokhmala, D. A. Shabanovbac

a Lomonosov Moscow State University
b MIPT
c National Research University "Higher School of Economics", Moscow
Full-text PDF (627 kB) Citations (4)
References:
Abstract: We study the threshold probability for the existence of a panchromatic coloring with $r$ colors for a random $k$-homogeneous hypergraph in the binomial model $ H (n, k, p) $, that is, a coloring such that each edge of the hypergraph contains the vertices of all $r$ colors. It is shown that this threshold probability for fixed $r<k$ and increasing $n$ corresponds to the sparse case, i. e. the case $p = cn/{n \choose k}$ for positive fixed $c$. Estimates of the form $ c_1 (r, k)<c<c_2 (r, k)$ for the parameter $c$ are found such that the difference $ c_2 (r, k) -c_1 (r, k) $ converges exponentially fast to zero if $r$ is fixed and $k$ tends to infinity.
Keywords: random hypergraph, panchromatic colorings, threshold probabilities, second moment method.
Funding agency Grant number
Russian Science Foundation 16-11-10014
Received: 11.02.2018
English version:
Discrete Mathematics and Applications, 2021, Volume 31, Issue 1, Pages 19–41
DOI: https://doi.org/10.1515/dma-2021-0003
Bibliographic databases:
Document Type: Article
UDC: 519.174+519.179.1+519.179.4
Language: Russian
Citation: D. A. Kravtsov, N. E. Krokhmal, D. A. Shabanov, “Panchromatic colorings of random hypergraphs”, Diskr. Mat., 31:2 (2019), 84–113; Discrete Math. Appl., 31:1 (2021), 19–41
Citation in format AMSBIB
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\paper Panchromatic colorings of random hypergraphs
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\jour Discrete Math. Appl.
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\pages 19--41
\crossref{https://doi.org/10.1515/dma-2021-0003}
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  • https://doi.org/10.4213/dm1504
  • https://www.mathnet.ru/eng/dm/v31/i2/p84
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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