# Forbidden Minors

### Some articles on forbidden, minors, forbidden minors, minor, forbidden minor:

Linkless Embedding - History
... who posed several related problems including the problem of finding a forbidden graph characterization of the graphs with linkless and flat embeddings Sachs showed that the seven graphs of ... embeddable graphs are closed under graph minors, from which it follows by the Robertsonâ€“Seymour theorem that a forbidden graph characterization exists ... of obstruction graphs does not lead to an explicit description of this set of forbidden minors, but it follows from Sachs' results that the seven graphs of the Petersen family belong to the ...
Path Decomposition - Graph Minors - Excluding A Forest
... If a family F of graphs is closed under taking minors (every minor of a member of F is also in F), then by the Robertsonâ€“Seymour theorem F can be characterized ... the complete graph K5 nor the complete bipartite graph K3,3 as minors ... with the existence of a forest in the family of forbidden minors ...
Branch-decomposition - Forbidden Minors
... theorem, the graphs of branchwidth k can be characterized by a finite set of forbidden minors ... The graphs of branchwidth 0 are the matchings the minimal forbidden minors are a two-edge path graph and a triangle graph (or the two-edge cycle, if multigraphs rather than simple ... are the graphs in which each connected component is a star the minimal forbidden minors for branchwidth 1 are the triangle graph (or the two-edge cycle, if multigraphs rather than simple ...
Tree Decomposition - Graph Minors
... any fixed constant k, the partial k-trees are closed under the operation of graph minors, and therefore, by the Robertsonâ€“Seymour theorem, this family can be characterized in terms of a finite set of forbidden minors ... For partial 1-trees (that is, forests), the single forbidden minor is a triangle, and for the partial 2-trees the single forbidden minor is the complete ... However, the number of forbidden minors increases for larger values of k ...

### Famous quotes containing the word forbidden:

I am forbidden sugar, fat, and alcohol. So hooray, I guess, for oatmeal, lemon juice, and chicken soup.
Mason Cooley (b. 1927)