On the Maximal Cut in a Random Hypergraph
This paper deals with the problem of finding the max-cut for random hypergraphs. We consider the classical binomial model of a random k -uniform hypergraph on n vertices with probability . The main results generalize previously known facts for the graph case and show that in the sparse case (when fo...
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| Veröffentlicht in: | Doklady. Mathematics 2021-11, Vol.104 (3), p.336-339 |
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| container_title | Doklady. Mathematics |
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| creator | Zakharov, P. A. Shabanov, D. A. |
| description | This paper deals with the problem of finding the max-cut for random hypergraphs. We consider the classical binomial model
of a random
k
-uniform hypergraph on
n
vertices with probability
. The main results generalize previously known facts for the graph case and show that in the sparse case (when
for some fixed
independent of
n
) there exists
such that the ratio of the maximal cut of
to the number of vertices converges in probability to
. Moreover, we obtain some bounds for the value of
. |
| doi_str_mv | 10.1134/S1064562421060181 |
| format | Article |
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of a random
k
-uniform hypergraph on
n
vertices with probability
. The main results generalize previously known facts for the graph case and show that in the sparse case (when
for some fixed
independent of
n
) there exists
such that the ratio of the maximal cut of
to the number of vertices converges in probability to
. Moreover, we obtain some bounds for the value of
.</description><identifier>ISSN: 1064-5624</identifier><identifier>EISSN: 1531-8362</identifier><identifier>DOI: 10.1134/S1064562421060181</identifier><language>eng</language><publisher>Moscow: Pleiades Publishing</publisher><subject>Apexes ; Graph theory ; Graphs ; Mathematics ; Mathematics and Statistics</subject><ispartof>Doklady. Mathematics, 2021-11, Vol.104 (3), p.336-339</ispartof><rights>Pleiades Publishing, Ltd. 2021. ISSN 1064-5624, Doklady Mathematics, 2021, Vol. 104, No. 3, pp. 336–339. © Pleiades Publishing, Ltd., 2021. Russian Text © The Author(s), 2021, published in Doklady Rossiiskoi Akademii Nauk. Matematika, Informatika, Protsessy Upravleniya, 2021, Vol. 501, pp. 26–30.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c246t-7791f881e18003de2dc9e9aaff40ab15a0e49276573ba93b45441dbc2be6c9a23</citedby><cites>FETCH-LOGICAL-c246t-7791f881e18003de2dc9e9aaff40ab15a0e49276573ba93b45441dbc2be6c9a23</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://link.springer.com/content/pdf/10.1134/S1064562421060181$$EPDF$$P50$$Gspringer$$H</linktopdf><linktohtml>$$Uhttps://link.springer.com/10.1134/S1064562421060181$$EHTML$$P50$$Gspringer$$H</linktohtml><link.rule.ids>314,780,784,27924,27925,41488,42557,51319</link.rule.ids></links><search><creatorcontrib>Zakharov, P. A.</creatorcontrib><creatorcontrib>Shabanov, D. A.</creatorcontrib><title>On the Maximal Cut in a Random Hypergraph</title><title>Doklady. Mathematics</title><addtitle>Dokl. Math</addtitle><description>This paper deals with the problem of finding the max-cut for random hypergraphs. We consider the classical binomial model
of a random
k
-uniform hypergraph on
n
vertices with probability
. The main results generalize previously known facts for the graph case and show that in the sparse case (when
for some fixed
independent of
n
) there exists
such that the ratio of the maximal cut of
to the number of vertices converges in probability to
. Moreover, we obtain some bounds for the value of
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of a random
k
-uniform hypergraph on
n
vertices with probability
. The main results generalize previously known facts for the graph case and show that in the sparse case (when
for some fixed
independent of
n
) there exists
such that the ratio of the maximal cut of
to the number of vertices converges in probability to
. Moreover, we obtain some bounds for the value of
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| ispartof | Doklady. Mathematics, 2021-11, Vol.104 (3), p.336-339 |
| issn | 1064-5624 1531-8362 |
| language | eng |
| recordid | cdi_proquest_journals_2645878355 |
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| subjects | Apexes Graph theory Graphs Mathematics Mathematics and Statistics |
| title | On the Maximal Cut in a Random Hypergraph |
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