Editing Robertson–Seymour theorem (section)

{{Short description|Finiteness of sets of forbidden graph minors}}
In [[graph theory]], the '''Robertson–Seymour theorem''' (also called the '''graph minors theorem'''<ref>{{harvtxt|Bienstock|Langston|1995}}.</ref>) states that the [[undirected graph]]s, [[partial order|partially ordered]] by the [[minor (graph theory)|graph minor]] relationship, form a [[well-quasi-ordering]].<ref>{{harvtxt|Robertson|Seymour|2004}}.</ref> Equivalently, every family of graphs that is closed under taking minors can be defined by a finite set of [[forbidden minor]]s, in the same way that [[Wagner's theorem]] characterizes the [[planar graph]]s as being the graphs that do not have the [[complete graph]] <math>K_5</math> or the [[complete bipartite graph]] <math>K_{3,3}</math> as minors.

The Robertson–Seymour theorem is named after mathematicians [[Neil Robertson (mathematician)|Neil Robertson]] and [[Paul Seymour (mathematician)|Paul D. Seymour]], who proved it in a series of twenty papers spanning over 500 pages from 1983 to 2004.<ref>{{harvs|last1=Robertson|last2=Seymour|year=1983|year2=2004|txt}}; {{harvtxt|Diestel|2005|p=333}}.</ref> Before its proof, the statement of the theorem was known as '''Wagner's conjecture''' after the German mathematician [[Klaus Wagner (mathematician)|Klaus Wagner]], although Wagner said he never conjectured it.<ref>{{harvtxt|Diestel|2005|p=355}}.</ref>

A weaker result for [[tree (graph theory)|trees]] is implied by [[Kruskal's tree theorem]], which was conjectured in 1937 by [[Andrew Vázsonyi]] and proved in 1960 independently by [[Joseph Kruskal]] and S. Tarkowski.<ref>{{harvtxt|Diestel|2005|pp=335–336}}; {{harvtxt|Lovász|2005}}, Section 3.3, pp. 78–79.</ref>