Excluding a Countable Clique
نویسندگان
چکیده
We extend the excluded Kn minor theorem of Robertson and Seymour to infinite graphs, and deduce a structural characterization of the infinite graphs that have no Kא0 minor. The latter is a refinement of an earlier characterization of Robertson, Seymour and the second author.
منابع مشابه
Clique-width of countable graphs: a compactness property
We de*ne the clique-width of a countable graph. We prove that a countable graph has *nite clique-width i+ its *nite induced subgraphs have bounded clique-width. We obtain an application to a conjecture concerning the structure of sets of countable graphs having a decidable monadic second-order satis*ability problem. c © 2003 Elsevier B.V. All rights reserved.
متن کاملGraph Structure and Monadic Second-Order Logic: Language Theoretical Aspects
Graph structure is a flexible concept covering many different types of graph properties. Hierarchical decompositions yielding the notions of tree-width and clique-width, expressed by terms written with appropriate graph operations and associated with Monadic Second-order Logic are important tools for the construction of Fixed-Parameter Tractable algorithms and also for the extension of methods ...
متن کاملApproximating Maximum Independent Sets by Excluding Subgraphs 1
An approximation algorithm for the maximum independent set problem is given, improving the best performance guarantee known to O(n=(logn) 2 ). We also obtain the same performance guarantee for graph coloring. The results can be combined into a surprisingly strong simultaneous performance guarantee for the clique and coloring problems. The framework of subgraph-excluding algorithms is presented....
متن کاملExcluding a near-clique and a near-anticlique
Ramsey’s theorem says that for every clique H1 and for every graph H2 with no edges, all graphs containing neither of H1, H2 as induced subgraphs have bounded size. What if, instead, we exclude a graph H1 with a vertex whose deletion gives a clique, and the complement H2 of another such graph? This no longer implies bounded size, but it implies tightly restricted structure that we describe. The...
متن کامل8 F eb 2 01 2 Cliques in Odd - Minor - Free Graphs ∗
This paper is about: (1) bounds on the number of cliques in a graph in a particular class, and (2) algorithms for listing all cliques in a graph. We present a simple algorithm that lists all cliques in an n-vertex graph in O(n) time per clique. For O(1)-degenerate graphs, such as graphs excluding a fixed minor, we describe a O(n) time algorithm for listing all cliques. We prove that graphs excl...
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:
- J. Comb. Theory, Ser. B
دوره 76 شماره
صفحات -
تاریخ انتشار 1999