Clique-width of countable graphs: a compactness property
نویسنده
چکیده
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.
منابع مشابه
Several notions of rank-width for countable graphs
We define several notions of rank-width for countable graphs. We compare, for each of them the width of a countable graph with the least upper-bound of the widths of its finite induced subgraphs. A width has the compactness property if these two values are equal. Our notion of rank-width that uses quasi-trees (trees where paths may have the order type of rational numbers) has this property. So ...
متن کاملCOUNTABLE COMPACTNESS AND THE LINDEL¨OF PROPERTY OF L-FUZZY SETS
In this paper, countable compactness and the Lindel¨of propertyare defined for L-fuzzy sets, where L is a complete de Morgan algebra. Theydon’t rely on the structure of the basis lattice L and no distributivity is requiredin L. A fuzzy compact L-set is countably compact and has the Lindel¨ofproperty. An L-set having the Lindel¨of property is countably compact if andonly if it is fuzzy compact. ...
متن کاملThe monadic second-order logic of graphs XIV: uniformly sparse graphs and edge set quanti*cations
We consider the class USk of uniformly k-sparse simple graphs, i.e., the class of *nite or countable simple graphs, every *nite subgraph of which has a number of edges bounded by k times the number of vertices. We prove that for each k, every monadic second-order formula (intended to express a graph property) that uses variables denoting sets of edges can be e7ectively translated into a monadic...
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 کاملOn the compactness property of extensions of first-order G"{o}del logic
We study three kinds of compactness in some variants of G"{o}del logic: compactness,entailment compactness, and approximate entailment compactness.For countable first-order underlying language we use the Henkinconstruction to prove the compactness property of extensions offirst-order g logic enriched by nullary connective or the Baaz'sprojection connective. In the case of uncountable first-orde...
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:
- Electronic Notes in Discrete Mathematics
دوره 5 شماره
صفحات -
تاریخ انتشار 2000