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Journal articles on the topic 'Problème de Turán'

Author: Grafiati

Published: 25 May 2024

Last updated: 31 July 2025

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1

KEEVASH, PETER, DHRUV MUBAYI, BENNY SUDAKOV, and JACQUES VERSTRAËTE. "Rainbow Turán Problems." Combinatorics, Probability and Computing 16, no. 01 (2006): 109. http://dx.doi.org/10.1017/s0963548306007760.

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2

Bollobás, Béla. "Turán-Ramsey problems." Discrete Mathematics 156, no. 1-3 (1996): 257–62. http://dx.doi.org/10.1016/0012-365x(96)00024-6.

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3

Keevash, Peter, Mike Saks, Benny Sudakov, and Jacques Verstraëte. "Multicolour Turán problems." Advances in Applied Mathematics 33, no. 2 (2004): 238–62. http://dx.doi.org/10.1016/j.aam.2003.08.005.

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4

Frankl, Peter, Hao Huang, and Vojtěch Rödl. "On local Turán problems." Journal of Combinatorial Theory, Series A 177 (January 2021): 105329. http://dx.doi.org/10.1016/j.jcta.2020.105329.

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5

BOLLOBÁS, BÉLA, IMRE LEADER, and CLAUDIA MALVENUTO. "Daisies and Other Turán Problems." Combinatorics, Probability and Computing 20, no. 5 (2011): 743–47. http://dx.doi.org/10.1017/s0963548311000319.

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Our aim in this note is to make some conjectures about extremal densities of daisy-free families, where a ‘daisy’ is a certain hypergraph. These questions turn out to be related to some Turán problems in the hypercube, but they are also natural in their own right. We start by giving the daisy conjectures, and some related problems, and shall then go on to describe the connection with vertex-Turán problems in the hypercube.

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6

Mubayi*, Dhruv, and Vojtěch Rödl†. "Supersaturation For Ramsey-Turán Problems." Combinatorica 26, no. 3 (2006): 315–32. http://dx.doi.org/10.1007/s00493-006-0018-x.

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7

Mubayi, Dhruv, and Yi Zhao. "Non-uniform Turán-type problems." Journal of Combinatorial Theory, Series A 111, no. 1 (2005): 106–10. http://dx.doi.org/10.1016/j.jcta.2004.11.010.

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8

Bennett, Patrick, Sean English, and Maria Talanda-Fisher. "Weighted Turán problems with applications." Discrete Mathematics 342, no. 8 (2019): 2165–72. http://dx.doi.org/10.1016/j.disc.2019.04.007.

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9

Frankl, Peter, and Jiaxi Nie. "On asymptotic local Turán problems." Moscow Journal of Combinatorics and Number Theory 12, no. 4 (2023): 273–86. http://dx.doi.org/10.2140/moscow.2023.12.273.

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10

Mani, Nitya, and Edward Yu. "Turán problems for mixed graphs." Journal of Combinatorial Theory, Series B 167 (July 2024): 119–63. http://dx.doi.org/10.1016/j.jctb.2024.02.004.

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11

Spiro, Sam, and Jacques Verstraëte. "Relative Turán Problems for Uniform Hypergraphs." SIAM Journal on Discrete Mathematics 35, no. 3 (2021): 2170–91. http://dx.doi.org/10.1137/20m1364631.

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12

Xu, Zixiang, Yifan Jing, and Gennian Ge. "On vertex-induced weighted Turán problems." Discrete Mathematics 345, no. 1 (2022): 112628. http://dx.doi.org/10.1016/j.disc.2021.112628.

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13

Peng, Xing, and Craig Timmons. "Infinite Turán Problems for Bipartite Graphs." SIAM Journal on Discrete Mathematics 28, no. 2 (2014): 702–10. http://dx.doi.org/10.1137/130922987.

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14

Cooper, Joshua, Dheer Noal Desai, and Anurag Sahay. "Principal eigenvectors in hypergraph Turán problems." Electronic Journal of Linear Algebra 40 (October 23, 2024): 697–713. http://dx.doi.org/10.13001/ela.2024.8497.

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For a general class of hypergraph Turán problems with uniformity $r$, we investigate the principal eigenvector for the $p$-spectral radius (in the sense of Keevash-Lenz-Mubayi and Nikiforov) for the extremal graphs, showing in a strong sense that these eigenvectors have close to equal weight on each vertex (equivalently, showing that the principal ratio is close to $1$). We investigate the sharpness of our result; it is likely sharp for the Turán tetrahedron problem. In the course of this latter discussion, we establish a lower bound on the $p$-spectral radius of an arbitrary $r$-graph in term

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15

Johnson, J. Robert, and John Talbot. "Vertex Turán problems in the hypercube." Journal of Combinatorial Theory, Series A 117, no. 4 (2010): 454–65. http://dx.doi.org/10.1016/j.jcta.2009.07.004.

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16

Kostochka, Alexandr, Dhruv Mubayi, and Jacques Verstraëte. "Turán problems and shadows II: Trees." Journal of Combinatorial Theory, Series B 122 (January 2017): 457–78. http://dx.doi.org/10.1016/j.jctb.2016.06.011.

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17

Gerbner, Dániel, Ervin Győri, Abhishek Methuku, and Máté Vizer. "Generalized Turán problems for even cycles." Journal of Combinatorial Theory, Series B 145 (November 2020): 169–213. http://dx.doi.org/10.1016/j.jctb.2020.05.005.

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18

Füredi, Zoltán, and André Kündgen. "Turán problems for integer-weighted graphs." Journal of Graph Theory 40, no. 4 (2002): 195–225. http://dx.doi.org/10.1002/jgt.10012.

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19

Gerbner, Dániel, Abhishek Methuku, Dániel T. Nagy, Dömötör Pálvölgyi, Gábor Tardos, and Máté Vizer. "Turán problems for edge-ordered graphs." Journal of Combinatorial Theory, Series B 160 (May 2023): 66–113. http://dx.doi.org/10.1016/j.jctb.2022.12.006.

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20

Gerbner, Dániel. "Generalized Turán problems for double stars." Discrete Mathematics 346, no. 7 (2023): 113395. http://dx.doi.org/10.1016/j.disc.2023.113395.

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21

Gerbner, Dániel, and Cory Palmer. "Some exact results for generalized Turán problems." European Journal of Combinatorics 103 (June 2022): 103519. http://dx.doi.org/10.1016/j.ejc.2022.103519.

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22

Gerbner, Dániel, Abhishek Methuku, Dániel T. Nagy, Balázs Patkós, and Máté Vizer. "Vertex Turán problems for the oriented hypercube." Acta Universitatis Sapientiae, Mathematica 13, no. 2 (2021): 356–66. http://dx.doi.org/10.2478/ausm-2021-0022.

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Abstract In this short note we consider the oriented vertex Turán problem in the hypercube: for a fixed oriented graph F → \vec F , determine the maximum cardinality e x v ( F → , Q → n ) e{x_v}\left( {\vec F,{{\vec Q}_n}} \right) of a subset U of the vertices of the oriented hypercube Q → n {\vec Q_n} such that the induced subgraph Q → n [ U ] {\vec Q_n}\left[ U \right] does not contain any copy of F → \vec F . We obtain the exact value of e x v ( P k , → Q n → ) e{x_v}\left( {\overrightarrow {{P_k},} \,\overrightarrow {{Q_n}} } \right) for the directed path P k → \overrightarrow {{P_k}} , th

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23

Balogh, József, Hong Liu, and Maryam Sharifzadeh. "On Two Problems in Ramsey--Turán Theory." SIAM Journal on Discrete Mathematics 31, no. 3 (2017): 1848–66. http://dx.doi.org/10.1137/16m1086078.

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24

Gerbner, Dániel. "On non-degenerate Turán problems for expansions." European Journal of Combinatorics 124 (February 2025): 104071. http://dx.doi.org/10.1016/j.ejc.2024.104071.

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25

Vértesi, P. "Turán type problems on mean convergence. II." Acta Mathematica Hungarica 65, no. 3 (1994): 237–42. http://dx.doi.org/10.1007/bf01875151.

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26

Bialostocki, A., and N. Sauer. "On Ramsey-Turán type problems in tournaments." Discrete Mathematics 59, no. 3 (1986): 221–28. http://dx.doi.org/10.1016/0012-365x(86)90168-8.

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27

Frankl, P., and Z. Füredi. "Exact solution of some Turán-type problems." Journal of Combinatorial Theory, Series A 45, no. 2 (1987): 226–62. http://dx.doi.org/10.1016/0097-3165(87)90016-1.

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28

MOSSINGHOFF, MICHAEL J., and TIMOTHY S. TRUDGIAN. "BETWEEN THE PROBLEMS OF PÓLYA AND TURÁN." Journal of the Australian Mathematical Society 93, no. 1-2 (2012): 157–71. http://dx.doi.org/10.1017/s1446788712000201.

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AbstractWe investigate the behaviour of the function $L_{\alpha }(x) = \sum _{n\leq x}\lambda (n)/n^{\alpha }$, where $\lambda (n)$ is the Liouville function and $\alpha $ is a real parameter. The case where $\alpha =0$ was investigated by Pólya; the case $\alpha =1$, by Turán. The question of the existence of sign changes in both of these cases is related to the Riemann hypothesis. Using both analytic and computational methods, we investigate similar problems for the more general family $L_{\alpha }(x)$, where $0\leq \alpha \leq 1$, and their relationship to the Riemann hypothesis and other p

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29

Li, H., V. Nikiforov, and R. H. Schelp. "A new class of Ramsey–Turán problems." Discrete Mathematics 310, no. 24 (2010): 3579–83. http://dx.doi.org/10.1016/j.disc.2010.09.009.

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30

Gerbner, Dániel, Abhishek Methuku, and Cory Palmer. "General lemmas for Berge–Turán hypergraph problems." European Journal of Combinatorics 86 (May 2020): 103082. http://dx.doi.org/10.1016/j.ejc.2020.103082.

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31

Balogh, József, Ce Chen, Grace McCourt, and Cassie Murley. "Ramsey–Turán problems with small independence numbers." European Journal of Combinatorics 118 (May 2024): 103872. http://dx.doi.org/10.1016/j.ejc.2023.103872.

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32

She, Chuan-Ming, Yi-Zheng Fan, and Liying Kang. "Spectral bipartite Turán problems on linear hypergraphs." Discrete Mathematics 348, no. 6 (2025): 114435. https://doi.org/10.1016/j.disc.2025.114435.

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33

Talbot, John. "Chromatic Turán problems and a new upper bound for the Turán density of K4−." European Journal of Combinatorics 28, no. 8 (2007): 2125–42. http://dx.doi.org/10.1016/j.ejc.2007.04.012.

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34

Ni, Zhenyu, Liying Kang, and Erfang Shan. "Turán Problems for Berge-(k, p)-Fan Hypergraph." Chinese Annals of Mathematics, Series B 42, no. 4 (2021): 487–94. http://dx.doi.org/10.1007/s11401-021-0272-7.

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35

Kostochka, Alexandr, Dhruv Mubayi, and Jacques Verstraëte. "Turán Problems and Shadows III: Expansions of Graphs." SIAM Journal on Discrete Mathematics 29, no. 2 (2015): 868–76. http://dx.doi.org/10.1137/140977138.

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36

Alon, Noga. "Erasure list-decodable codes and Turán hypercube problems." Finite Fields and Their Applications 100 (December 2024): 102513. http://dx.doi.org/10.1016/j.ffa.2024.102513.

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37

Sudakov, Benny. "A few remarks on Ramsey–Turán-type problems." Journal of Combinatorial Theory, Series B 88, no. 1 (2003): 99–106. http://dx.doi.org/10.1016/s0095-8956(02)00038-2.

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38

Schelp, R. H. "Some Ramsey–Turán type problems and related questions." Discrete Mathematics 312, no. 14 (2012): 2158–61. http://dx.doi.org/10.1016/j.disc.2011.09.015.

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39

Gerbner, Dániel, Abhishek Methuku, and Máté Vizer. "Generalized Turán problems for disjoint copies of graphs." Discrete Mathematics 342, no. 11 (2019): 3130–41. http://dx.doi.org/10.1016/j.disc.2019.06.022.

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40

Shangguan, Chong, and Itzhak Tamo. "New Turán Exponents for Two Extremal Hypergraph Problems." SIAM Journal on Discrete Mathematics 34, no. 4 (2020): 2338–45. http://dx.doi.org/10.1137/20m1325769.

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41

Kostochka, Alexandr, Dhruv Mubayi, and Jacques Verstraëte. "Turán problems and shadows I: Paths and cycles." Journal of Combinatorial Theory, Series A 129 (January 2015): 57–79. http://dx.doi.org/10.1016/j.jcta.2014.09.005.

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42

Keevash, Peter. "A hypergraph regularity method for generalized Turán problems." Random Structures and Algorithms 34, no. 1 (2009): 123–64. http://dx.doi.org/10.1002/rsa.20249.

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43

Sidorenko, Alexander. "On Turán problems for Cartesian products of graphs." Journal of Combinatorial Designs 27, no. 7 (2019): 411–14. http://dx.doi.org/10.1002/jcd.21651.

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44

Gerbner, Dániel. "On the extremal graphs in generalized Turán problems." Discrete Mathematics 347, no. 6 (2024): 114021. http://dx.doi.org/10.1016/j.disc.2024.114021.

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45

Zhou, Junpeng, and Xiying Yuan. "Turán problems for star-path forests in hypergraphs." Discrete Mathematics 348, no. 11 (2025): 114592. https://doi.org/10.1016/j.disc.2025.114592.

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46

Gerbner, Dániel, Casey Tompkins, and Junpeng Zhou. "On hypergraph Turán problems with bounded matching number." European Journal of Combinatorics 127 (June 2025): 104155. https://doi.org/10.1016/j.ejc.2025.104155.

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47

Andersson, J. "On some power sum problems of Turán and Erdős." Acta Mathematica Hungarica 70, no. 4 (1996): 305–16. http://dx.doi.org/10.1007/bf02187393.

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48

Palmer, Cory, Michael Tait, Craig Timmons, and Adam Zsolt Wagner. "Turán numbers for Berge-hypergraphs and related extremal problems." Discrete Mathematics 342, no. 6 (2019): 1553–63. http://dx.doi.org/10.1016/j.disc.2019.02.003.

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49

Gyárfás, András. "Ramsey and Turán-type problems in bipartite geometric graphs." Electronic Notes in Discrete Mathematics 31 (August 2008): 253–54. http://dx.doi.org/10.1016/j.endm.2008.06.051.

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50

Mubayi, Dhruv, and Vera T. Sós. "Explicit constructions of triple systems for Ramsey–Turán problems." Journal of Graph Theory 52, no. 3 (2006): 211–16. http://dx.doi.org/10.1002/jgt.20156.

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