Optimizing the Graph Minors Weak Structure Theorem
نویسندگان
چکیده
منابع مشابه
Optimizing the Graph Minors Weak Structure Theorem
Abstract. One of the major results of [N. Robertson and P. D. Seymour. Graph minors. XIII. The disjoint paths problem. J. Combin. Theory Ser. B, 63(1):65–110, 1995], also known as the weak structure theorem, reveals the local structure of graphs excluding some graph as a minor: each such graph G either has small treewidth or contains the subdivision of a planar graph (a wall) that can be arrang...
متن کاملComplete graph minors and the graph minor structure theorem
Article history: Received 19 May 2011 Available online xxxx
متن کاملAn accessibility theorem for infinite graph minors
In his recent collection [ 2 ] of open problems about infinite graphs, Halin defines the following hierarchy of graphs. He defines Γ0 to be the class of all graphs (finite or infinite), and for each ordinal μ > 0 he defines Γμ as the class of all graphs containing, for each λ < μ, infinitely many disjoint connected graphs from Γλ. Thus, Γ1 is the class of infinite graphs, Γ2 is the class of all...
متن کاملGraph minors. VIII. A kuratowski theorem for general surfaces
Kuratowski’s famous theorem of 1930 [6] asserts that a graph is planar if and only if it does not topologically contain K5 or K3,3. (Graphs are finite, and may have loops or multiple edges. A graph G topologically contains H if we may obtain a graph isomorphic to H from some subgraph of G by suppressing some divalent vertices.) There arose in the 1930’s the proposal to lind parallels to this th...
متن کاملGraph Minors
For a given graph G and integers b, f ≥ 0, let S be a subset of vertices of G of size b + 1 such that the subgraph of G induced by S is connected and S can be separated from other vertices of G by removing f vertices. We prove that every graph on n vertices contains at most n/ b+f b such vertex subsets. This result from extremal combinatorics appears to be very useful in the design of several e...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2013
ISSN: 0895-4801,1095-7146
DOI: 10.1137/110857027