From: stl137@aol.com (STL137) Newsgroups: sci.math Subject: Re: What is ramsey number r(4,5)? Date: 31 Oct 1998 18:39:51 GMT Here is a listing of all the Ramsey numbers currently known or being worked on. R(3,3)=6 R(3,4)=9 R(3,5)=14 R(3,6)=18 R(3,7)=23 R(3,8)=28 R(3,9)=36 R(3,10)=40 to 43 R(4,4)=18 R(4,5)=25 R(4,6)=35 to 41 R(5,5)=43 to 49 R(5,6)=58 to 87 R(6,6)=102 to 165 R(7,7)=205 to 540 Where R(number of acquaintances, number of strangers). So the answer to your question is 25. ------ STL137@aol.com ===> Website: http://members.aol.com/stl137/ PGP keys: ~~~pgp.html Quotes: ~~~quotes.html "I have sworn upon the altar of God eternal hostility against every form of tyranny over the mind of man" - Thomas Jefferson ============================================================================== From: hwatheod@leland.Stanford.EDU (theodore hwa) Newsgroups: sci.math,comp.theory Subject: Re: Known Ramsey numbers Date: 24 Nov 1998 07:55:48 GMT Dave Rusin (rusin@vesuvius.math.niu.edu) wrote: : wrote: : >Is there a recent paper or recent book or web-site of a researcher : >which lists all currently known Ramsey numbers? : : From: tessa : Newsgroups: sci.math : Subject: Re: Graph Theory : Date: 1 Dec 1997 21:58:05 GMT : : The Journal of Graph Theory, Spring 1983 contains 19 papers about Ramsey : and Ramsey numbers. [...] : upper and lower bounds are known for : r(3,8)=28-29 I remember being told that r(3,8) is known to be 28, proven by computer search about 7 or 8 years ago. Sorry, no reference at hand. Ted ============================================================================== From: Juergen Stuber Newsgroups: sci.math,comp.theory Subject: Re: Known Ramsey numbers Date: 24 Nov 1998 13:46:07 +0100 marissablumentha@hotmail.com writes: > > Is there a recent paper or recent book or web-site of a researcher > which lists all currently known Ramsey numbers? http://bmb-fs1.biochem.okstate.edu/OAS/OJAS/jstone.htm states R(5,5)=50 and has some references. J�rgen -- J�rgen Stuber http://www.mpi-sb.mpg.de/~juergen/ ============================================================================== From: yerman@advicom.antispam.net (Niall Graham) Newsgroups: sci.math,comp.theory Subject: Re: Known Ramsey numbers Date: 24 Nov 1998 19:51:55 -0600 J�rgen Stuber writes >http://bmb-fs1.biochem.okstate.edu/OAS/OJAS/jstone.htm >states R(5,5)=50 and has some references. Gasp. I think you are a victim of a language barrier (?) The current best known bounds are 43 <= R(5,5) <= 49 I met an expert on the subject a couple of years ago who believes 43 is the correct answer. Niall Graham ============================================================================== From: Juergen Stuber Newsgroups: sci.math,comp.theory Subject: Re: Known Ramsey numbers Date: 25 Nov 1998 14:22:18 +0100 yerman@advicom.antispam.net (Niall Graham) writes: > > J�rgen Stuber writes > > >http://bmb-fs1.biochem.okstate.edu/OAS/OJAS/jstone.htm > >states R(5,5)=50 and has some references. Note the careful wording. I didn't write 'proves'. > Gasp. I think you are a victim of a language barrier (?) I don't think so. > The current best known bounds are > > 43 <= R(5,5) <= 49 > > I met an expert on the subject a couple of years ago who > believes 43 is the correct answer. Then the guy who wrote that paper made some mistake, though on a first glance it looks quite solid. He exhibits a graph of 49 nodes with edges in two colors that, as he states, contains no complete subgraph of 5 nodes in one color. Probably he hasn't checked this carefully enough. Such a graph would show R(5,5)>49, and he has R(5,5)<=50 from some other source. J�rgen -- J�rgen Stuber http://www.mpi-sb.mpg.de/~juergen/ ============================================================================== Newsgroups: sci.math,comp.theory From: tromp@cwi.nl (John Tromp) Subject: Re: Known Ramsey numbers Date: Wed, 25 Nov 1998 13:50:01 GMT Juergen Stuber writes: >yerman@advicom.antispam.net (Niall Graham) writes: >> >> Juergen Stuber writes >> >> >http://bmb-fs1.biochem.okstate.edu/OAS/OJAS/jstone.htm >> >states R(5,5)=50 and has some references. >Then the guy who wrote that paper made some mistake, >though on a first glance it looks quite solid. >He exhibits a graph of 49 nodes with edges in two colors that, >as he states, contains no complete subgraph of 5 nodes in one color. I checked his results about a year ago and found them to be erroneous. He claims that a cyclic pattern of edge colors BBBRRRBBBRRRBRBRBRBRBRBRRBRBRBRBRBRBRRRBBBRRRBBB (from node i to nodes i+1, i+2, ... , i-1 mod 49) is free from a Red or Blue K_5. BBBRRRBBBRRRBRBRBRBRBRBRRBRBRBRBRBRBRRRBBBRRRBBB 0 7 1 2 4 5 8 1 Consider nodes 0, 7, 15, 28, and 41. This is a Blue K_5, since for instance the edge from 7 to 28 is the same color as from 0 to 21 which is Blue. The same for all other differences {7,8,13,21,26,34}. I recall sending the author email about this but never getting a response. It turns out that cyclic color patterns are not very good for showing lower bounds; at best the pattern 0111011011100011000000001100011101101110 shows that R(5,5) > 41. regards, %!PS % -John Tromp (http://www.cwi.nl/~tromp/) 42 42 scale 7 9 translate .07 setlinewidth .5 setgray/c{arc clip fill setgray}def 1 0 0 42 1 0 c 0 1 1{0 3 3 90 270 arc 0 0 6 0 -3 3 90 270 arcn 270 90 c -2 2 4{-6 moveto 0 12 rlineto}for -5 2 5{-3 exch moveto 9 0 rlineto}for stroke 0 0 3 1 1 0 c 180 rotate initclip}for showpage ============================================================================== From: cd@sun-graphe.lri.fr (Charles Delorme) Newsgroups: sci.math,comp.theory Subject: Re: Known Ramsey numbers Date: 27 Nov 1998 09:07:21 GMT In article <73cbje$2qo$1@nnrp1.dejanews.com>, marissablumentha@hotmail.com writes: |> Is there a recent paper or recent book or web-site of a researcher |> which lists all currently known Ramsey numbers? |> |> Thank you. |> |> -----------== Posted via Deja News, The Discussion Network ==---------- |> http://www.dejanews.com/ Search, Read, Discuss, or Start Your Own You could look at Geoffrey Exoo page http://isu.indstate.edu/ge/RAM/index.html to have some recent constructions, and to Dynamic Surveys, http://www.combinatorics.org/Surveys/index.html Article 1, by Stanislaw Radziszowski contains a lot of results with their reference. -- Charles Delorme tous les megalomanes LRI ont une signature cd@lri.fr a etages