Obstruction sets for outer-cylindrical graphs
نویسندگان
چکیده
A graph is outer-cylindrical if it embeds in the sphere so that there are two distinct faces whose boundaries together contain all the vertices. The class of outer-cylindrical graphs is closed under minors. We give the complete set of 38 minor-minimal non-outer-cylindrical graphs, or equivalently, an excluded minor characterization of outercylindrical graphs. We also give the obstruction sets under the related topological ordering and Y -ordering.
منابع مشابه
Obstruction Sets for Outer-Projective-Planar Graphs
A graph G is outer projective planar if it can be embedded in the projective plane so that every vertex appears on the boundary of a single face We exhibit obstruction sets for outer projective planar graphs with respect to the subdivision minor and Y orderings Equivalently we nd the minimal non outer projective planar graphs under these orderings
متن کاملEffective Computation of Immersion Obstructions for Unions of Graph Classes
In the final paper of the Graph Minors series N. Robertson and P. Seymour proved that graphs are well-quasi-ordered under the immersion ordering. A direct implication of this theorem is that each class of graphs that is closed under taking immersions can be fully characterized by forbidding a finite set of graphs (immersion obstruction set). However, as the proof of the well-quasi-ordering theo...
متن کاملForbidden minors to graphs with small feedback sets
Finite obstruction set characterizations for lower ideals in the minor order are guaranteed to exist by the Graph Minor Theorem. In this paper we characterize several families of graphs with small feedback sets, namely k1-Feedback Vertex Set, k2-Feedback Edge Set and (k1,k2){Feedback Vertex/Edge Set, for small integer parameters k1 and k2. Our constructive methods can compute obstruction sets f...
متن کاملOn computing graph minor obstruction sets
The Graph Minor Theorem of Robertson and Seymour establishes nonconstructively that many natural graph properties are characterized by a nite set of forbidden substructures, the obstructions for the property. We prove several general theorems regarding the computation of obstruction sets from other information about a family of graphs. The methods can be adapted to other partial orders on graph...
متن کاملComparison of Two Kinds of Functionally Graded Cylindrical Shells with Various Volume Fraction Laws for Vibration Analysis
In this paper, a study on the vibration of thin cylindrical shells made of a functionally gradient material (FGM) composed of stainless steel and nickel is presented. The effects of the FGM configuration are taken into account by studying the frequencies of two FG cylindrical shells. Type I FG cylindrical shell has nickel on its inner surface and stainless steel on its outer surface and Type II...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Journal of Graph Theory
دوره 38 شماره
صفحات -
تاریخ انتشار 2001