Search results
Results From The WOW.Com Content Network
The Robertson–Seymour theorem states that finite undirected graphs and graph minors form a well-quasi-ordering. The graph minor relationship does not contain any infinite descending chain, because each contraction or deletion reduces the number of edges and vertices of the graph (a non-negative integer). [8]
In graph theory, an undirected graph H is called a minor of the graph G if H can be formed from G by deleting edges, vertices and by contracting edges. The theory of graph minors began with Wagner's theorem that a graph is planar if and only if its minors include neither the complete graph K 5 nor the complete bipartite graph K 3,3. [1]
In mathematics, the graph structure theorem is a major result in the area of graph theory. The result establishes a deep and fundamental connection between the theory of graph minors and topological embeddings. The theorem is stated in the seventeenth of a series of 23 papers by Neil Robertson and Paul Seymour. Its proof is very long and involved.
These graph classes include planar graphs, map graphs, bounded-genus graphs and graphs excluding any fixed minor. In particular, bidimensionality theory builds on the graph minor theory of Robertson and Seymour by extending the mathematical results and building new algorithmic tools. The theory was introduced in the work of Demaine, Fomin ...
This states that families of graphs closed under the graph minor operation may be characterized by a finite set of forbidden minors. As part of this work, Robertson and Seymour also proved the graph structure theorem describing the graphs in these families. [6] Additional major results in Robertson's research include the following:
Algorithmically, the problem of recognizing linkless and flat embeddable graphs was settled once the forbidden minor characterization was proven: an algorithm of Robertson & Seymour (1995) can be used to test in polynomial time whether a given graph contains any of the seven forbidden minors. [18]
Pages in category "Graph minor theory" The following 33 pages are in this category, out of 33 total. ... Robertson–Seymour theorem; S. Shallow minor; Snark (graph ...
In the language of the later papers in Robertson and Seymour's graph minor series, a path-decomposition is a tree decomposition (X,T) in which the underlying tree T of the decomposition is a path graph.