See also ·Ramsey cardinal Paris-Harrington theorem ·Sim(pencil game)) Infinite Ramsey theory Van der Waerden number ·Ramsey game Erdos -Rado theorem Notes 1.Some authors restrict the values to be greater than one.for example(Brualdi 2010)and(Harar 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 (Erd6s Szekeres 1935).In this form,the consideration of graphs with one vertex is more natural. 2.up to automorphisms of the araph 3.D an(2006)."pa au/Publ/Gaze te/200 /Nov06/Nov06. p "Party Acquaintances"(http://www.cut-the-knot.org/Curriculum/Combinatorics/ThreeOrThree.sh tml#nequality2) 5."Ramsey Graphs"(http://cs.anu.edu.au/-bdm/data/ramsey.html). 6.2.6 Ramsey Theory from Mathematics Illuminated(http://www.learner.org/channel/courses/math illuminated/units/2/textbook/06.php) 7.Brendan D.McKay.Stanislaw P.Radziszowski(May 1995)."R(4,5)=25"(htp://users.cecs.anu edu au-hd s/rA5 df (PDE)loumal of Granh The /1gQ1200 doi10.1002jgt3190190304htps:1doi.0rg10.1002%2Fjgt3190190304). 8.Ex00 98.doi10.1002jgt3190130113ht lower bound for R(5,5) Journal of Graph Theory.13(1):97- doi.0rg/10.10029%2Fjgt3190130113). 9.Vigleik Angeltveit;Brendan McKay(2017)."R(5,5)<48".arXiv:1703.08768v2(https://arxiv.or g/abs/1703.08768v2)[math.CO (https://arxiv.org/archive/math.CO)]. 10.Joel H.Spencer(1994),Ten Lectures on the Probabilistic Method (https://archive.org/details/ten lecturesonpro0000spen/page/4),SIAM,p.4(https://archive.org/details/tenlecturesonpro0000sp en/page/4),ISBN978-0-89871-325-1 11 Brendan d.McKay.sStanistaw P Radziszowski (1997)"Subaraph Countina ldentities and Ramsey Numbers"(http://cs.anu.edu.au/-bdm/papers/r55.pdf)(PDF).Journal of Combinatorial The0y.69(2y:193-209.doi1:10.1006/jctb.1996.1741htps:ldoi.org/10.1006%2 Fjctb.1996.174 1) 12.Radziszowski,Stanislaw(2011)."Small Ramsey Numbers"(http://www.combinatorics.org/ojs/i ndex.php/eljclarticle/view/DS1/pdf).Dynamic Surveys.Electronic Journal of Combinatorics. doi:10.37236/21htps:ldo1.0rg/10.37236%2F21) 13 Exoo Geoffrev Tatarevic Milos (2015)"N ds for 28 classical Ramse Numbers"(htp:ww combinatorics prlisndppelicarticlewiew22i3cnic Journal of Combinatorics.22 (3):3.arXiv:1504.02403(https://arxiv.org/abs/1504.02403). Bibcode:2015arXiv150402403E(https://ui.adsabs.harvard.edu/abs/2015arXiv150402403E) doi:10.37236/5254htps:/doi.0rg/10.37236%2F5254) 14.Martin Gould."Ramsey Theory"(http://people.maths.ox.ac.uk/-gouldm/ramsey.pdf)(PDF).Ramsey cardinal Paris–Harrington theorem Sim (pencil game) Infinite Ramsey theory Van der Waerden number Ramsey game Erdős–Rado theorem 1. 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. 2. up to automorphisms of the graph 3. Do, Norman (2006). "Party problems and Ramsey theory" (http://www.austms.org.au/Publ/Gaze tte/2006/Nov06/Nov06.pdf#page=17) (PDF). Austr. Math. Soc. Gazette. 33 (5): 306–312. 4. "Party Acquaintances" (http://www.cut-the-knot.org/Curriculum/Combinatorics/ThreeOrThree.sh tml#inequality2). 5. "Ramsey Graphs" (http://cs.anu.edu.au/~bdm/data/ramsey.html). 6. 2.6 Ramsey Theory from Mathematics Illuminated (http://www.learner.org/channel/courses/math illuminated/units/2/textbook/06.php) 7. Brendan D. McKay, Stanislaw P. Radziszowski (May 1995). "R(4,5) = 25" (http://users.cecs.anu. edu.au/~bdm/papers/r45.pdf) (PDF). Journal of Graph Theory. 19 (3): 309–322. doi:10.1002/jgt.3190190304 (https://doi.org/10.1002%2Fjgt.3190190304). 8. Exoo, Geoffrey (March 1989). "A lower bound for R(5, 5)". Journal of Graph Theory. 13 (1): 97– 98. doi:10.1002/jgt.3190130113 (https://doi.org/10.1002%2Fjgt.3190130113). 9. Vigleik Angeltveit; Brendan McKay (2017). " ". arXiv:1703.08768v2 (https://arxiv.or g/abs/1703.08768v2) [math.CO (https://arxiv.org/archive/math.CO)]. 10. Joel H. Spencer (1994), Ten Lectures on the Probabilistic Method (https://archive.org/details/ten lecturesonpro0000spen/page/4), SIAM, p. 4 (https://archive.org/details/tenlecturesonpro0000sp en/page/4), ISBN 978-0-89871-325-1 11. Brendan D. McKay, Stanisław P. Radziszowski (1997). "Subgraph Counting Identities and Ramsey Numbers" (http://cs.anu.edu.au/~bdm/papers/r55.pdf) (PDF). Journal of Combinatorial Theory. 69 (2): 193–209. doi:10.1006/jctb.1996.1741 (https://doi.org/10.1006%2Fjctb.1996.174 1). 12. Radziszowski, Stanisław (2011). "Small Ramsey Numbers" (http://www.combinatorics.org/ojs/i ndex.php/eljc/article/view/DS1/pdf). Dynamic Surveys. Electronic Journal of Combinatorics. doi:10.37236/21 (https://doi.org/10.37236%2F21). 13. Exoo, Geoffrey; Tatarevic, Milos (2015). "New Lower Bounds for 28 Classical Ramsey Numbers" (http://www.combinatorics.org/ojs/index.php/eljc/article/view/v22i3p11). Electronic Journal of Combinatorics. 22 (3): 3. arXiv:1504.02403 (https://arxiv.org/abs/1504.02403). Bibcode:2015arXiv150402403E (https://ui.adsabs.harvard.edu/abs/2015arXiv150402403E). doi:10.37236/5254 (https://doi.org/10.37236%2F5254). 14. Martin Gould. "Ramsey Theory" (http://people.maths.ox.ac.uk/~gouldm/ramsey.pdf) (PDF). See also Notes