Well-Quasi-Orderings and the Robertson–Seymour Theorems

As we will see, well-quasi-orderings (WQOs) provide a powerful engine for demonstrating that classes of problems are FPT. In the next section, we will look at the rudiments of the theory of WQOs, and in subsequent sections, we will examine applications to combinatorial problems.

[1]  Michael R. Fellows,et al.  On search decision and the efficiency of polynomial-time algorithms , 1989, STOC '89.

[2]  Graham Higman,et al.  Ordering by Divisibility in Abstract Algebras , 1952 .

[3]  C. Nash-Williams On well-quasi-ordering infinite trees , 1963, Mathematical Proceedings of the Cambridge Philosophical Society.

[4]  J. W. Kennedy,et al.  The theorem on planar graphs , 1985 .

[5]  Michael J. Dinneen,et al.  A Characterization of Graphs with Vertex Cover up to Five , 1994, ORDAL.

[6]  Bojan Mohar,et al.  Embedding graphs in an arbitrary surface in linear time , 1996, STOC '96.

[7]  Frank Harary,et al.  Graph Theory , 2016 .

[8]  Michael R. Fellows,et al.  Parameterized Complexity , 1998 .

[9]  Neil Robertson,et al.  Graph Minors .XIII. The Disjoint Paths Problem , 1995, J. Comb. Theory B.

[10]  C. Kuratowski Sur le problème des courbes gauches en Topologie , 1930 .

[11]  Michael R. Fellows,et al.  Obstructions to Within a Few Vertices or Edges of Acyclic , 1995, WADS.

[12]  H. Rice Classes of recursively enumerable sets and their decision problems , 1953 .

[13]  Paul Wollan,et al.  Finding topological subgraphs is fixed-parameter tractable , 2010, STOC '11.

[14]  Robin Thomas,et al.  Well-quasi-ordering infinite graphs with forbidden finite planar minor , 1989 .

[15]  Bruno Courcelle,et al.  A Note on the Computability of Graph Minor Obstruction Sets for Monadic Second Order Ideals , 1997, J. Univers. Comput. Sci..

[16]  Frank Plumpton Ramsey,et al.  On a Problem of Formal Logic , 1930 .

[17]  Michael R. Fellows,et al.  Nonconstructive tools for proving polynomial-time decidability , 1988, JACM.

[18]  Marcin Kaminski,et al.  Chain Minors Are FPT , 2013, IPEC.

[19]  K. Wagner Über eine Eigenschaft der ebenen Komplexe , 1937 .

[20]  Detlef Seese,et al.  The Structure of Models of Decidable Monadic Theories of Graphs , 1991, Ann. Pure Appl. Log..

[21]  Paul D. Seymour,et al.  Graph Minors: XV. Giant Steps , 1996, J. Comb. Theory, Ser. B.

[22]  Michael R. Fellows,et al.  Nonconstructive Advances in Polynomial-Time Complexity , 1987, Inf. Process. Lett..

[23]  R. Rado Partial well-ordering of sets of vectors , 1954 .

[24]  Michael R. Fellows,et al.  On computing graph minor obstruction sets , 2000, Theor. Comput. Sci..

[25]  J. Gustedt Well Quasi Ordering Finite Posets and Formal Languages , 1995, J. Comb. Theory, Ser. B.

[26]  J. Kruskal Well-quasi-ordering, the Tree Theorem, and Vazsonyi’s conjecture , 1960 .

[27]  Michael R. Fellows,et al.  Finite automata, bounded treewidth, and well-quasiordering , 1991, Graph Structure Theory.

[28]  Paul D. Seymour,et al.  Graph Minors. XX. Wagner's conjecture , 2004, J. Comb. Theory B.

[29]  G. Dirac,et al.  A Theorem of Kuratowski , 1954 .

[30]  Joseph B. Kruskal,et al.  The Theory of Well-Quasi-Ordering: A Frequently Discovered Concept , 1972, J. Comb. Theory A.