Ramsey's theorem (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Ramsey's theorem" in English language version.

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ams.org

bookstore.ams.org

"The Triangle-Free Process and the Ramsey Number $R (3, k)$ ". bookstore.ams.org. Retrieved 2023-06-27.

mathscinet.ams.org

Dushnik, Ben; Miller, E. W. (1941). "Partially ordered sets". American Journal of Mathematics. 63 (3): 600–610. doi:10.2307/2371374. hdl:10338.dmlcz/100377. JSTOR 2371374. MR 0004862.. See in particular Theorems 5.22 and 5.23.

anu.edu.au

cs.anu.edu.au

"Ramsey Graphs".
Brendan D. McKay, Stanisław P. Radziszowski (1997). "Subgraph Counting Identities and Ramsey Numbers" (PDF). Journal of Combinatorial Theory. Series B. 69 (2): 193–209. doi:10.1006/jctb.1996.1741.

users.cecs.anu.edu.au

McKay, Brendan D.; Radziszowski, Stanislaw P. (May 1995). "R(4,5) = 25" (PDF). Journal of Graph Theory. 19 (3): 309–322. doi:10.1002/jgt.3190190304.

archive.org

Joel H. Spencer (1994), Ten Lectures on the Probabilistic Method, SIAM, p. 4, ISBN 978-0-89871-325-1

arxiv.org

Montanaro, Ashley (2016). "Quantum algorithms: an overview". npj Quantum Information. 2 (1): 15023. arXiv:1511.04206. Bibcode:2016npjQI...215023M. doi:10.1038/npjqi.2015.23. S2CID 2992738 – via Nature.
Wang, Hefeng (2016). "Determining Ramsey numbers on a quantum computer". Physical Review A. 93 (3): 032301. arXiv:1510.01884. Bibcode:2016PhRvA..93c2301W. doi:10.1103/PhysRevA.93.032301. S2CID 118724989.
Vigleik Angeltveit; Brendan McKay (September 2024). " $R(5,5)\leq 46$ ". arXiv:2409.15709 [math.CO].
Angeltveit, Vigleik (31 Dec 2023). " $R(3,10)\leq 41$ ". arXiv:2401.00392 [math.CO].
Exoo, Geoffrey; Tatarevic, Milos (2015). "New Lower Bounds for 28 Classical Ramsey Numbers". Electronic Journal of Combinatorics. 22 (3): 3. arXiv:1504.02403. Bibcode:2015arXiv150402403E. doi:10.37236/5254.
Exoo, Geoffrey (26 Oct 2023). "A Lower Bound for R(5,6)". arXiv:2310.17099 [math.CO].
Campos, Marcelo; Griffiths, Simon; Morris, Robert; Sahasrabudhe, Julian (2023). "An exponential improvement for diagonal Ramsey". arXiv:2303.09521 [math.CO].
Bohman, Tom; Keevash, Peter (2020-11-17). "Dynamic concentration of the triangle-free process". Random Structures and Algorithms. 58 (2): 221–293. arXiv:1302.5963. doi:10.1002/rsa.20973.
Bohman, Tom; Keevash, Peter (2010-08-01). "The early evolution of the H-free process". Inventiones Mathematicae. 181 (2): 291–336. arXiv:0908.0429. Bibcode:2010InMat.181..291B. doi:10.1007/s00222-010-0247-x. ISSN 1432-1297.
Mattheus, Sam; Verstraete, Jacques (5 Mar 2024). "The asymptotics of r(4,t)". Annals of Mathematics. 199 (2). arXiv:2306.04007. doi:10.4007/annals.2024.199.2.8.
Gauthier, Thibault; Brown, Chad E (2024), "A formal proof of R(4,5)=25", arXiv preprint, arXiv:2404.01761
Fox, Jacob; Sudakov, Benny (2008). "Induced Ramsey-type theorems". Advances in Mathematics. 219 (6): 1771–1800. arXiv:0706.4112. doi:10.1016/j.aim.2008.07.009.
Conlon, David; Fox, Jacob; Sudakov, Benny (2012). "On two problems in graph Ramsey theory". Combinatorica. 32 (5): 513–535. arXiv:1002.0045. doi:10.1007/s00493-012-2710-3.
Conlon, David; Fox, Jacob; Zhao, Yufei (May 2014). "Extremal results in sparse pseudorandom graphs". Advances in Mathematics. 256: 206–29. arXiv:1204.6645. doi:10.1016/j.aim.2013.12.004.
Fox, Jacob; Sudakov, Benny (2009). "Density theorems for bipartite graphs and related Ramsey-type results". Combinatorica. 29 (2): 153–196. arXiv:0707.4159v2. doi:10.1007/s00493-009-2475-5.
Conlon, David; Dellamonica Jr., Domingos; La Fleur, Steven; Rödl, Vojtěch; Schacht, Mathias (2017). "A note on induced Ramsey numbers". In Loebl, Martin; Nešetřil, Jaroslav; Thomas, Robin (eds.). A Journey Through Discrete Mathematics. Springer, Cham. pp. 357–366. arXiv:1601.01493. doi:10.1007/978-3-319-44479-6_13. ISBN 978-3-319-44478-9.
Neiman, David; Mackey, John; Heule, Marijn (2020-11-01). "Tighter Bounds on Directed Ramsey Number R(7)". arXiv:2011.00683 [math.CO].

austms.org.au

Do, Norman (2006). "Party problems and Ramsey theory" (PDF). Austr. Math. Soc. Gazette. 33 (5): 306–312.

cambridge.org

Blass, Andreas (September 1977). "Ramsey's theorem in the hierarchy of choice principles". The Journal of Symbolic Logic. 42 (3): 387–390. doi:10.2307/2272866. ISSN 1943-5886. JSTOR 2272866.

combinatorics.org

Radziszowski, Stanisław (2011). "Small Ramsey Numbers". Dynamic Surveys. Electronic Journal of Combinatorics. 1000. doi:10.37236/21.
Exoo, Geoffrey; Tatarevic, Milos (2015). "New Lower Bounds for 28 Classical Ramsey Numbers". Electronic Journal of Combinatorics. 22 (3): 3. arXiv:1504.02403. Bibcode:2015arXiv150402403E. doi:10.37236/5254.

cut-the-knot.org

"Party Acquaintances".

doi.org

Some authors restrict the values to be greater than one, for example (Brualdi 2010) and (Harary 1972), thus avoiding a discussion of edge colouring a graph with no edges, while others rephrase the statement of the theorem to require, in a simple graph, either an $r$ -clique or an $s$ -independent set, see (Gross 2008) or (Erdős & Szekeres 1935). In this form, the consideration of graphs with one vertex is more natural. Brualdi, Richard A. (2010), Introductory Combinatorics (5th ed.), Prentice-Hall, pp. 77–82, ISBN 978-0-13-602040-0 Harary, Frank (1972), Graph Theory, Addison-Wesley, pp. 16–17, ISBN 0-201-02787-9 Gross, Jonathan L. (2008), Combinatorial Methods with Computer Applications, CRC Press, p. 458, ISBN 978-1-58488-743-0 Erdős, Paul; Szekeres, George (1935), "A combinatorial problem in geometry" (PDF), Compositio Mathematica, 2: 463–470, doi:10.1007/978-0-8176-4842-8_3, ISBN 978-0-8176-4841-1.
Radziszowski, Stanisław (2011). "Small Ramsey Numbers". Dynamic Surveys. Electronic Journal of Combinatorics. 1000. doi:10.37236/21.
Montanaro, Ashley (2016). "Quantum algorithms: an overview". npj Quantum Information. 2 (1): 15023. arXiv:1511.04206. Bibcode:2016npjQI...215023M. doi:10.1038/npjqi.2015.23. S2CID 2992738 – via Nature.
Wang, Hefeng (2016). "Determining Ramsey numbers on a quantum computer". Physical Review A. 93 (3): 032301. arXiv:1510.01884. Bibcode:2016PhRvA..93c2301W. doi:10.1103/PhysRevA.93.032301. S2CID 118724989.
McKay, Brendan D.; Radziszowski, Stanislaw P. (May 1995). "R(4,5) = 25" (PDF). Journal of Graph Theory. 19 (3): 309–322. doi:10.1002/jgt.3190190304.
Exoo, Geoffrey (March 1989). "A lower bound for $R (5, 5)$ ". Journal of Graph Theory. 13 (1): 97–98. doi:10.1002/jgt.3190130113.
Brendan D. McKay, Stanisław P. Radziszowski (1997). "Subgraph Counting Identities and Ramsey Numbers" (PDF). Journal of Combinatorial Theory. Series B. 69 (2): 193–209. doi:10.1006/jctb.1996.1741.
Exoo, Geoffrey; Tatarevic, Milos (2015). "New Lower Bounds for 28 Classical Ramsey Numbers". Electronic Journal of Combinatorics. 22 (3): 3. arXiv:1504.02403. Bibcode:2015arXiv150402403E. doi:10.37236/5254.
Ajtai, Miklós; Komlós, János; Szemerédi, Endre (1980-11-01). "A note on Ramsey numbers". Journal of Combinatorial Theory, Series A. 29 (3): 354–360. doi:10.1016/0097-3165(80)90030-8. ISSN 0097-3165.
Kim, Jeong Han (1995), "The Ramsey Number R(3,t) has order of magnitude t²/log t", Random Structures and Algorithms, 7 (3): 173–207, CiteSeerX 10.1.1.46.5058, doi:10.1002/rsa.3240070302
Bohman, Tom; Keevash, Peter (2020-11-17). "Dynamic concentration of the triangle-free process". Random Structures and Algorithms. 58 (2): 221–293. arXiv:1302.5963. doi:10.1002/rsa.20973.
Bohman, Tom; Keevash, Peter (2010-08-01). "The early evolution of the H-free process". Inventiones Mathematicae. 181 (2): 291–336. arXiv:0908.0429. Bibcode:2010InMat.181..291B. doi:10.1007/s00222-010-0247-x. ISSN 1432-1297.
Mattheus, Sam; Verstraete, Jacques (5 Mar 2024). "The asymptotics of r(4,t)". Annals of Mathematics. 199 (2). arXiv:2306.04007. doi:10.4007/annals.2024.199.2.8.
Erdös, Paul (1990), Nešetřil, Jaroslav; Rödl, Vojtěch (eds.), "Problems and Results on Graphs and Hypergraphs: Similarities and Differences", Mathematics of Ramsey Theory, Algorithms and Combinatorics, vol. 5, Berlin, Heidelberg: Springer, pp. 12–28, doi:10.1007/978-3-642-72905-8_2, ISBN 978-3-642-72905-8, retrieved 2023-06-27
Kohayakawa, Y.; Prömel, H.J.; Rödl, V. (1998). "Induced Ramsey Numbers" (PDF). Combinatorica. 18 (3): 373–404. doi:10.1007/PL00009828.
Fox, Jacob; Sudakov, Benny (2008). "Induced Ramsey-type theorems". Advances in Mathematics. 219 (6): 1771–1800. arXiv:0706.4112. doi:10.1016/j.aim.2008.07.009.
Conlon, David; Fox, Jacob; Sudakov, Benny (2012). "On two problems in graph Ramsey theory". Combinatorica. 32 (5): 513–535. arXiv:1002.0045. doi:10.1007/s00493-012-2710-3.
Beck, József (1990). "On Size Ramsey Number of Paths, Trees and Circuits. II". In Nešetřil, J.; Rödl, V. (eds.). Mathematics of Ramsey Theory. Algorithms and Combinatorics. Vol. 5. Springer, Berlin, Heidelberg. pp. 34–45. doi:10.1007/978-3-642-72905-8_4. ISBN 978-3-642-72907-2.
Łuczak, Tomasz; Rödl, Vojtěch (March 1996). "On induced Ramsey numbers for graphs with bounded maximum degree". Journal of Combinatorial Theory. Series B. 66 (2): 324–333. doi:10.1006/jctb.1996.0025.
Conlon, David; Fox, Jacob; Zhao, Yufei (May 2014). "Extremal results in sparse pseudorandom graphs". Advances in Mathematics. 256: 206–29. arXiv:1204.6645. doi:10.1016/j.aim.2013.12.004.
Fox, Jacob; Sudakov, Benny (2009). "Density theorems for bipartite graphs and related Ramsey-type results". Combinatorica. 29 (2): 153–196. arXiv:0707.4159v2. doi:10.1007/s00493-009-2475-5.
Conlon, David; Dellamonica Jr., Domingos; La Fleur, Steven; Rödl, Vojtěch; Schacht, Mathias (2017). "A note on induced Ramsey numbers". In Loebl, Martin; Nešetřil, Jaroslav; Thomas, Robin (eds.). A Journey Through Discrete Mathematics. Springer, Cham. pp. 357–366. arXiv:1601.01493. doi:10.1007/978-3-319-44479-6_13. ISBN 978-3-319-44478-9.
Dushnik, Ben; Miller, E. W. (1941). "Partially ordered sets". American Journal of Mathematics. 63 (3): 600–610. doi:10.2307/2371374. hdl:10338.dmlcz/100377. JSTOR 2371374. MR 0004862.. See in particular Theorems 5.22 and 5.23.
Dybizbański, Janusz (2018-12-31). "A lower bound on the hypergraph Ramsey number R(4,5;3)". Contributions to Discrete Mathematics. 13 (2). doi:10.11575/cdm.v13i2.62416. ISSN 1715-0868.
Blass, Andreas (September 1977). "Ramsey's theorem in the hierarchy of choice principles". The Journal of Symbolic Logic. 42 (3): 387–390. doi:10.2307/2272866. ISSN 1943-5886. JSTOR 2272866.
Forster, T.E.; Truss, J.K. (January 2007). "Ramsey's theorem and König's Lemma". Archive for Mathematical Logic. 46 (1): 37–42. doi:10.1007/s00153-006-0025-z. ISSN 1432-0665.

erdosproblems.com

"Erdős Problems". www.erdosproblems.com. Retrieved 2023-07-12.

handle.net

hdl.handle.net

Dushnik, Ben; Miller, E. W. (1941). "Partially ordered sets". American Journal of Mathematics. 63 (3): 600–610. doi:10.2307/2371374. hdl:10338.dmlcz/100377. JSTOR 2371374. MR 0004862.. See in particular Theorems 5.22 and 5.23.

harvard.edu

ui.adsabs.harvard.edu

Montanaro, Ashley (2016). "Quantum algorithms: an overview". npj Quantum Information. 2 (1): 15023. arXiv:1511.04206. Bibcode:2016npjQI...215023M. doi:10.1038/npjqi.2015.23. S2CID 2992738 – via Nature.
Wang, Hefeng (2016). "Determining Ramsey numbers on a quantum computer". Physical Review A. 93 (3): 032301. arXiv:1510.01884. Bibcode:2016PhRvA..93c2301W. doi:10.1103/PhysRevA.93.032301. S2CID 118724989.
Exoo, Geoffrey; Tatarevic, Milos (2015). "New Lower Bounds for 28 Classical Ramsey Numbers". Electronic Journal of Combinatorics. 22 (3): 3. arXiv:1504.02403. Bibcode:2015arXiv150402403E. doi:10.37236/5254.
Bohman, Tom; Keevash, Peter (2010-08-01). "The early evolution of the H-free process". Inventiones Mathematicae. 181 (2): 291–336. arXiv:0908.0429. Bibcode:2010InMat.181..291B. doi:10.1007/s00222-010-0247-x. ISSN 1432-1297.

jstor.org

Dushnik, Ben; Miller, E. W. (1941). "Partially ordered sets". American Journal of Mathematics. 63 (3): 600–610. doi:10.2307/2371374. hdl:10338.dmlcz/100377. JSTOR 2371374. MR 0004862.. See in particular Theorems 5.22 and 5.23.
Blass, Andreas (September 1977). "Ramsey's theorem in the hierarchy of choice principles". The Journal of Symbolic Logic. 42 (3): 387–390. doi:10.2307/2272866. ISSN 1943-5886. JSTOR 2272866.

learner.org

2.6 Ramsey Theory from Mathematics Illuminated

nature.com

Montanaro, Ashley (2016). "Quantum algorithms: an overview". npj Quantum Information. 2 (1): 15023. arXiv:1511.04206. Bibcode:2016npjQI...215023M. doi:10.1038/npjqi.2015.23. S2CID 2992738 – via Nature.

numdam.org

Some authors restrict the values to be greater than one, for example (Brualdi 2010) and (Harary 1972), thus avoiding a discussion of edge colouring a graph with no edges, while others rephrase the statement of the theorem to require, in a simple graph, either an $r$ -clique or an $s$ -independent set, see (Gross 2008) or (Erdős & Szekeres 1935). In this form, the consideration of graphs with one vertex is more natural. Brualdi, Richard A. (2010), Introductory Combinatorics (5th ed.), Prentice-Hall, pp. 77–82, ISBN 978-0-13-602040-0 Harary, Frank (1972), Graph Theory, Addison-Wesley, pp. 16–17, ISBN 0-201-02787-9 Gross, Jonathan L. (2008), Combinatorial Methods with Computer Applications, CRC Press, p. 458, ISBN 978-1-58488-743-0 Erdős, Paul; Szekeres, George (1935), "A combinatorial problem in geometry" (PDF), Compositio Mathematica, 2: 463–470, doi:10.1007/978-0-8176-4842-8_3, ISBN 978-0-8176-4841-1.

ox.ac.uk

people.maths.ox.ac.uk

Gould, Martin. "Ramsey Theory" (PDF). Mathematical Institute, University of Oxford. Archived from the original (PDF) on 2022-01-30.

psu.edu

citeseerx.ist.psu.edu

Kim, Jeong Han (1995), "The Ramsey Number R(3,t) has order of magnitude t²/log t", Random Structures and Algorithms, 7 (3): 173–207, CiteSeerX 10.1.1.46.5058, doi:10.1002/rsa.3240070302

quantamagazine.org

Sloman, Leila (2 May 2023). "A Very Big Small Leap Forward in Graph Theory". Quanta Magazine.
Cepelewicz, Jordana (22 June 2023). "Mathematicians Discover Novel Way to Predict Structure in Graphs". Quanta Magazine.

rangevoting.org

Smith, Warren D.; Exoo, Geoff, Partial Answer to Puzzle #27: A Ramsey-like quantity, retrieved 2020-06-02

renyi.hu

users.renyi.hu

Erdős, Paul (1984). "On some problems in graph theory, combinatorial analysis and combinatorial number theory" (PDF). Graph Theory and Combinatorics: 1–17.

rit.edu

cs.rit.edu

Stanisław Radziszowski. "DS1". Retrieved 17 August 2023.

semanticscholar.org

api.semanticscholar.org

Montanaro, Ashley (2016). "Quantum algorithms: an overview". npj Quantum Information. 2 (1): 15023. arXiv:1511.04206. Bibcode:2016npjQI...215023M. doi:10.1038/npjqi.2015.23. S2CID 2992738 – via Nature.
Wang, Hefeng (2016). "Determining Ramsey numbers on a quantum computer". Physical Review A. 93 (3): 032301. arXiv:1510.01884. Bibcode:2016PhRvA..93c2301W. doi:10.1103/PhysRevA.93.032301. S2CID 118724989.

springer.com

link.springer.com

Forster, T.E.; Truss, J.K. (January 2007). "Ramsey's theorem and König's Lemma". Archive for Mathematical Logic. 46 (1): 37–42. doi:10.1007/s00153-006-0025-z. ISSN 1432-0665.

umd.edu

cs.umd.edu

Kohayakawa, Y.; Prömel, H.J.; Rödl, V. (1998). "Induced Ramsey Numbers" (PDF). Combinatorica. 18 (3): 373–404. doi:10.1007/PL00009828.

web.archive.org

Gould, Martin. "Ramsey Theory" (PDF). Mathematical Institute, University of Oxford. Archived from the original (PDF) on 2022-01-30.

worldcat.org

search.worldcat.org

Ajtai, Miklós; Komlós, János; Szemerédi, Endre (1980-11-01). "A note on Ramsey numbers". Journal of Combinatorial Theory, Series A. 29 (3): 354–360. doi:10.1016/0097-3165(80)90030-8. ISSN 0097-3165.
Bohman, Tom; Keevash, Peter (2010-08-01). "The early evolution of the H-free process". Inventiones Mathematicae. 181 (2): 291–336. arXiv:0908.0429. Bibcode:2010InMat.181..291B. doi:10.1007/s00222-010-0247-x. ISSN 1432-1297.
Dybizbański, Janusz (2018-12-31). "A lower bound on the hypergraph Ramsey number R(4,5;3)". Contributions to Discrete Mathematics. 13 (2). doi:10.11575/cdm.v13i2.62416. ISSN 1715-0868.
Blass, Andreas (September 1977). "Ramsey's theorem in the hierarchy of choice principles". The Journal of Symbolic Logic. 42 (3): 387–390. doi:10.2307/2272866. ISSN 1943-5886. JSTOR 2272866.
Forster, T.E.; Truss, J.K. (January 2007). "Ramsey's theorem and König's Lemma". Archive for Mathematical Logic. 46 (1): 37–42. doi:10.1007/s00153-006-0025-z. ISSN 1432-0665.