Definable decompositions for graphs of bounded linear cliquewidth
نویسندگان
چکیده
We prove that for every positive integer k, there exists an mso1-transduction that given a graph of linear cliquewidth at most k outputs, nondeterministically, some clique decomposition of the graph of width bounded by a function of k. A direct corollary of this result is the equivalence of the notions of cmso1-definability and recognizability on graphs of bounded linear cliquewidth.
منابع مشابه
Clique-width of full bubble model graphs
A bubble model is a 2-dimensional representation of proper interval graphs. We consider proper interval graphs that have bubble models of specific properties. We characterise the maximal such proper interval graphs of bounded clique-width and of bounded linear cliquewidth and the minimal such proper interval graphs whose clique-width and linear cliquewidth exceed the bounds. As a consequence, w...
متن کاملSpace and circuit complexity of monadic second-order definable problemes on tree-decomposable structures
A famous theorem of Courcelle states that every problem that is definable in monadic second-order (mso) logic can be solved in linear time on input structures of bounded tree width. While Courcelle’s result is optimal from the algorithmic point of view, this thesis shows how to solve monadic secondorder definable decision, counting, and optimization problems on tree-widthbounded structures opti...
متن کاملMSOL-Definability Equals Recognizability for Halin Graphs and Bounded Degree k-Outerplanar Graphs
One of the most famous algorithmic meta-theorems states that every graph property that can be defined by a sentence in counting monadic second order logic (CMSOL) can be checked in linear time for graphs of bounded treewidth, which is known as Courcelle’s Theorem [8]. These algorithms are constructed as finite state tree automata, and hence every CMSOL-definable graph property is recognizable. ...
متن کاملBounded Persistence Pathwidth
The role of graph width metrics, such as treewidth, pathwidth, and cliquewidth, is now seen as central in both algorithm design and the delineation of what is algorithmically possible. In this article we introduce a new, related, parameter for graphs, persistence. A path decomposition of width k, in which every vertex of the underlying graph belongs to at most l nodes of the path, has pathwidth...
متن کاملLinear Clique-width for Subclasses of Cographs, with Connections to Permutations
We prove that a hereditary property of cographs has bounded linear cliquewidth if and only if it does not contain all quasi-threshold graphs or their complements. The proof borrows ideas from the enumeration of permutation classes, and the similarities between these two strands of investigation lead us to a conjecture relating the graph properties of bounded linear clique-width to permutation c...
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:
دوره شماره
صفحات -
تاریخ انتشار 2018