@Article{         1994,
  Author        = "Latka, Brenda J.",
  Abstract      = "Given a finite relational language L is there an algorithm that, given two finite sets A and B of structures in the language, determines how many homogeneous L structures there are omitting every structure in B and embedding every structure in A? For directed graphs this question reduces to: Is there an algorithm that, given a finite set of tournaments Γ, determines whether QΓ, the class of finite tournaments omitting every tournament in Γ, is well-quasi-order? First, we give a nonconstructive proof of the existence of an algorithm for the case in which Γ consists of one tournament. Then we determine explicitly the set of tournaments each of which does not have an antichain omitting it. Two antichains are exhibited and a summary is given of two structure theorems which allow the application of Kruskal's Tree Theorem. Detailed proofs of these structure theorems will be given elsewhere. The case in which Γ consists of two tournaments is also discussed.",
  copyright     = "Copyright {\copyright} 1994 Association for Symbolic Logic",
  date-added    = "2015-03-04 09:32:13 +0000",
  date-modified = "2015-03-04 09:32:55 +0000",
  ISSN          = "00224812",
  Journal       = "The Journal of Symbolic Logic",
  jstor_formatteddate="Mar., 1994",
  Keywords      = "infinite antichains and tournament",
  Language      = "English",
  Number        = "1",
  Pages         = "pp. 124-139",
  Publisher     = "Association for Symbolic Logic",
  Title         = "Finitely Constrained Classes of Homogeneous Directed Graphs",
  URL           = "http://www.jstor.org/stable/2275255",
  Volume        = "59",
  Year          = "1994",
  bdsk-url-1    = "http://www.jstor.org/stable/2275255",
  File          = "Finitely Constrained Classes of Homogeneous Directed Graphs - Latka (0) (0) - a - a - y.pdf"
}

@Article{ 1994, Author = "Latka, Brenda J.", Abstract = "Given a finite relational language L is there an algorithm that, given two finite sets A and B of structures in the language, determines how many homogeneous L structures there are omitting every structure in B and embedding every structure in A? For directed graphs this question reduces to: Is there an algorithm that, given a finite set of tournaments Γ, determines whether QΓ, the class of finite tournaments omitting every tournament in Γ, is well-quasi-order? First, we give a nonconstructive proof of the existence of an algorithm for the case in which Γ consists of one tournament. Then we determine explicitly the set of tournaments each of which does not have an antichain omitting it. Two antichains are exhibited and a summary is given of two structure theorems which allow the application of Kruskal's Tree Theorem. Detailed proofs of these structure theorems will be given elsewhere. The case in which Γ consists of two tournaments is also discussed.", copyright = "Copyright {\copyright} 1994 Association for Symbolic Logic", date-added = "2015-03-04 09:32:13 +0000", date-modified = "2015-03-04 09:32:55 +0000", ISSN = "00224812", Journal = "The Journal of Symbolic Logic", jstor_formatteddate="Mar., 1994", Keywords = "infinite antichains and tournament", Language = "English", Number = "1", Pages = "pp. 124-139", Publisher = "Association for Symbolic Logic", Title = "Finitely Constrained Classes of Homogeneous Directed Graphs", URL = "http://www.jstor.org/stable/2275255", Volume = "59", Year = "1994", bdsk-url-1 = "http://www.jstor.org/stable/2275255", File = "Finitely Constrained Classes of Homogeneous Directed Graphs - Latka (0) (0) - a - a - y.pdf" }