Talk:Robertson–Seymour theorem

message: There was a request on Planetmath about merging this entry. The following was commented:
The status of Robertson-Seymour theorem seems to be very fuzzy at the moment. They have claimed to possess a proof sometime in 1980's, and the started publishing a long series of papers to establish it. So far they have not published the proof in its entirety, and what they published is published with the longest delayed I have seen ever (for example, ``Minors 18 were submitted on 5 June 1990, and published in 2003; ``Minors 15 were submitted on 15 March 1992, and published in 1996, i.e., they were submitted _two years after_ the paper they used the results from it). At such rate when (or whether) the proof will be published is questionable. So, I would hesitate to call the Wagner's conjecture to be Robertson-Seymour theorem.
''
Can anyone comment if this was really proved and if this theorem has been acknowledged as such by the mathematical community?
--Drini 23:12, 20 Feb 2005 (UTC)
thread_title: Merging

message: I propose to move this article back to Robertson-Seymour theorem, instead of its current location Robertson%E2%80%93Seymour_theorem. Actually, I do not see the point of having a non-ascii character that is almost the same of - instead of -. - Liberatore(T) 17:22, 18 March 2006 (UTC)
thread_title: Move

message: The Consequences section restates ideas.  Sometimes something is restated 3 times!  The motivation behind this seems to be that it may make the material easier to understand.  However, it makes the text take longer to read.  The only reason I can see that something is being restated is that technical terms are used and they may not be understood by some.  It is much prefered (by me at least) to use more linking which would better enable the reader to discover the meanings of technical terms.  --GrimRC 86.4.53.107 15:18, 25 July 2006 (UTC)
thread_title:  [[Robertson%E2%80%93Seymour_theorem#Consequences|Consequences]] 

message: This article says the following sets of finite graphs are downwardly closed:
*The set of all graphs that are disjoint unions of paths
*The set of all forests
*The set of all planar graphs
*The set of all outerplanar graphs
*The set of all graphs that can be embedded without edge intersections in a torus
*the set of all graphs that can be embedded without edge intersections in a fixed arbitrary surface S
*the set of all graphs that are knotlessly embeddable in Euclidean 3-space
*the set of all graphs that are linklessly embeddable in Euclidean 3-space
The theorem says that in each such case there's a finite set of forbidden minors.  I think the article should state explicitly what the set of forbidden minors is in each case.  I know what they are in the case of planar graphs; I used to know in at least a couple of other cases---I'd have to dig out some old notes if I can find them. Michael Hardy 23:30, 19 April 2007 (UTC)
thread_title:  missing information 

message: Does anyone know if R-S theorem allows for graphs with loops (i.e., graphs with edges going in and out from the same vertex)?
Are the results still valid for directed graphs? And for multigraphs?
Thanks,
Jose Brox  —Preceding unsigned comment added by 88.0.102.184 (talk) 22:08, 7 April 2009 (UTC)
thread_title:  Generalizations? 

message: We can simply enumerate all obstruction sets until the right one is found. Since it always exists, this can be done in finite time. Now the algorithm is constructive. The only problem is whether we can recognize the right obstruction set when we see it. Wangzirui (talk) 16:00, 3 January 2011 (UTC)
replies: text: It may be "the only problem", but it is a problem, one that prevents this from being an algorithm and from being constructive. —David Eppstein (talk) 20:05, 3 January 2011 (UTC)
thread_title:  Non-constructive?