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A note on panchromatic colorings. / Cherkashin, Danila.

In: Discrete Mathematics, Vol. 341, No. 3, 01.03.2018, p. 652-657.

Research output: Contribution to journal › Article › peer-review

Harvard

Cherkashin, D 2018, 'A note on panchromatic colorings', Discrete Mathematics, vol. 341, no. 3, pp. 652-657. https://doi.org/10.1016/j.disc.2017.10.030

APA

Cherkashin, D. (2018). A note on panchromatic colorings. Discrete Mathematics, 341(3), 652-657. https://doi.org/10.1016/j.disc.2017.10.030

Vancouver

Cherkashin D. A note on panchromatic colorings. Discrete Mathematics. 2018 Mar 1;341(3):652-657. https://doi.org/10.1016/j.disc.2017.10.030

Author

Cherkashin, Danila. / A note on panchromatic colorings. In: Discrete Mathematics. 2018 ; Vol. 341, No. 3. pp. 652-657.

BibTeX

@article{8803612c35734de891ae7ca998a3b6f7,
title = "A note on panchromatic colorings",
abstract = "This paper studies the quantity p(n,r), that is the minimal number of edges of an n-uniform hypergraph without panchromatic coloring (it means that every edge meets every color) in r colors. If [Formula presented] then all bounds have a type [Formula presented], where A1, A2 are some algebraic fractions. The main result is a new lower bound on p(n,r) when r is at least cn; we improve an upper bound on p(n,r) if n=o(r3∕2). Also we show that p(n,r) has upper and lower bounds depending only on n∕r when the ratio n∕r is small, which cannot be reached by the previous probabilistic machinery. Finally we construct an explicit example of a hypergraph without panchromatic coloring and with [Formula presented].",
keywords = "Hypergraph colorings, Panchromatic colorings, EDGES, UNIFORM HYPERGRAPHS",
author = "Danila Cherkashin",
year = "2018",
month = mar,
day = "1",
doi = "10.1016/j.disc.2017.10.030",
language = "English",
volume = "341",
pages = "652--657",
journal = "Discrete Mathematics",
issn = "0012-365X",
publisher = "Elsevier",
number = "3",

}

RIS

TY - JOUR

T1 - A note on panchromatic colorings

AU - Cherkashin, Danila

PY - 2018/3/1

Y1 - 2018/3/1

N2 - This paper studies the quantity p(n,r), that is the minimal number of edges of an n-uniform hypergraph without panchromatic coloring (it means that every edge meets every color) in r colors. If [Formula presented] then all bounds have a type [Formula presented], where A1, A2 are some algebraic fractions. The main result is a new lower bound on p(n,r) when r is at least cn; we improve an upper bound on p(n,r) if n=o(r3∕2). Also we show that p(n,r) has upper and lower bounds depending only on n∕r when the ratio n∕r is small, which cannot be reached by the previous probabilistic machinery. Finally we construct an explicit example of a hypergraph without panchromatic coloring and with [Formula presented].

AB - This paper studies the quantity p(n,r), that is the minimal number of edges of an n-uniform hypergraph without panchromatic coloring (it means that every edge meets every color) in r colors. If [Formula presented] then all bounds have a type [Formula presented], where A1, A2 are some algebraic fractions. The main result is a new lower bound on p(n,r) when r is at least cn; we improve an upper bound on p(n,r) if n=o(r3∕2). Also we show that p(n,r) has upper and lower bounds depending only on n∕r when the ratio n∕r is small, which cannot be reached by the previous probabilistic machinery. Finally we construct an explicit example of a hypergraph without panchromatic coloring and with [Formula presented].

KW - Hypergraph colorings

KW - Panchromatic colorings

KW - EDGES

KW - UNIFORM HYPERGRAPHS

UR - http://www.scopus.com/inward/record.url?scp=85035814485&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2017.10.030

DO - 10.1016/j.disc.2017.10.030

M3 - Article

AN - SCOPUS:85035814485

VL - 341

SP - 652

EP - 657

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 3

ER -

ID: 35109964