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Matematicheskie Zametki, 2014, Volume 95, Issue 2, Pages 271–281
DOI: https://doi.org/10.4213/mzm10187 (Mi mzm10187) 		 
This article is cited in 2 scientific papers (total in 2 papers)

On Turán's (3,4)-Problem with Forbidden Subgraphs

A. A. Razborovab

a Steklov Mathematical Institute of the Russian Academy of Sciences
b University of Chicago, USA
Full-text PDF (485 kB) Citations (2)
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DOI: https://doi.org/10.4213/mzm10187
Abstract: We identify three 3-graphs on five vertices that are missing in all known extremal configurations for Turán's (3,4)-problem and prove Turán's conjecture for 3-graphs that are additionally known not to contain any induced copies of these 3-graphs. Our argument is based on an (apparently) new technique of “indirect interpretation” that allows us to retrieve additional structure from hypothetical counterexamples to Turán's conjecture, but in rather loose and limited sense. We also include two miscellaneous calculations in flag algebras that prove similar results about some other additional forbidden subgraphs.
Keywords: Turán's (3,4)-problem, 3-graph, hypergraph, forbidden subgraph.
Funding agency Grant number
Russian Foundation for Basic Research
Received: 13.12.2012
Revised: 23.03.2013
English version:
Mathematical Notes, 2014, Volume 95, Issue 2, Pages 247–254
DOI: https://doi.org/10.1134/S000143461401026X
Bibliographic databases:
Document Type: Article
UDC: 519.113
Language: Russian
Citation: A. A. Razborov, “On Turán's (3,4)-Problem with Forbidden Subgraphs”, Mat. Zametki, 95:2 (2014), 271–281; Math. Notes, 95:2 (2014), 247–254
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm10187
  • https://www.mathnet.ru/eng/mzm/v95/i2/p271
    • This publication is cited in the following 2 articles:
    1. A. Raymond, J. Saunderson, M. Singh, R. R. Thomas, “Symmetric sums of squares over k-subset hypercubes”, Math. Program., 167:2 (2018), 315–354  crossref  mathscinet  zmath  isi  scopus
    2. Norin S., Yepremyan L., “Sparse Halves in Dense Triangle-Free Graphs”, J. Comb. Theory Ser. B, 115 (2015), 1–25  crossref  mathscinet  zmath  isi  elib  scopus
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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