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Diskretnyi Analiz i Issledovanie Operatsii, 2022, Volume 29, Issue 1, Pages 46–55
DOI: https://doi.org/10.33048/daio.2022.29.723 (Mi da1292) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On the maximum number of open triangles in graphs with the same number of vertices and edges

A. V. Pyatkinab, O. I. Chernykhb

a Sobolev Institute of Mathematics, 4 Acad. Koptyug Avenue, 630090 Novosibirsk, Russia
b Novosibirsk State University, 2 Pirogov Street, 630090 Novosibirsk, Russia
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DOI: https://doi.org/10.33048/daio.2022.29.723
Abstract: An open triangle (OT) is a $3$-vertex subgraph with two edges, i. e. an induced path of length $2$. A formula for the maximum number of OT in $n$-vertex graphs with $n$ edges is proved in the paper. We also present a full characterization of graphs for which the maximum is attained. Illustr. 2, bibliogr. 10.
Keywords: open triangles, induced subgraphs, unicyclic graphs.
Funding agency Grant number
Russian Foundation for Basic Research 20-01-00045
This work was supported by the Russian Foundation for Basic Research, project no. 20-01-00045.
Received: 26.07.2021
Revised: 27.09.2021
Accepted: 28.09.2021
English version:
Journal of Applied and Industrial Mathematics, 2022, Volume 16, Issue 1, Pages 116–121
DOI: https://doi.org/10.1134/S1990478922010112
Document Type: Article
UDC: 519.17
Language: Russian
Citation: A. V. Pyatkin, O. I. Chernykh, “On the maximum number of open triangles in graphs with the same number of vertices and edges”, Diskretn. Anal. Issled. Oper., 29:1 (2022), 46–55; J. Appl. Industr. Math., 16:1 (2022), 116–121
Citation in format AMSBIB
\Bibitem{PyaChe22}
\by A.~V.~Pyatkin, O.~I.~Chernykh
\paper On the maximum number of open triangles in~graphs with the same number of~vertices~and~edges
\jour Diskretn. Anal. Issled. Oper.
\yr 2022
\vol 29
\issue 1
\pages 46--55
\mathnet{http://mi.mathnet.ru/da1292}
\crossref{https://doi.org/10.33048/daio.2022.29.723}
\transl
\jour J. Appl. Industr. Math.
\yr 2022
\vol 16
\issue 1
\pages 116--121
\crossref{https://doi.org/10.1134/S1990478922010112}
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