Turán, involution and shifting

Gil Kalai, Eran Nevo

Research output: Contribution to journalArticlepeer-review


We propose a strengthening of the conclusion in Turán’s (3,4)-conjecture in terms of algebraic shifting, and show that its analogue for graphs does hold. In another direction, we generalize the Mantel–Turán theorem by weakening its assumption: for any graph G on n vertices and any involution on its vertex set, if for any 3-set S of the vertices, the number of edges in G spanned by S, plus the number of edges in G spanned by the image of S under the involution, is at least 2, then the number of edges in G is at least the Mantel–Turán bound, namely the number achieved by two disjoint cliques of sizes n2 rounded up and down.

Original languageAmerican English
Pages (from-to)367-378
Number of pages12
JournalAlgebraic Combinatorics
Issue number3
StatePublished - 2019

Bibliographical note

Funding Information:
Acknowledgements. Research of Kalai is partially supported by ERC advanced grant 320924, BSF grant 2006066, and NSF grant DMS-1300120, and of Nevo by Israel Science Foundation grant ISF-1695/15, by grant 2528/16 of the ISF-NRF Singapore joint research program, and by ISF-BSF joint grant 2016288.

Publisher Copyright:
© The journal and the authors, 2019.


  • Shifting
  • Threshold graphs
  • Turán’s (3,4)-conjecture


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