Clique-width and edge contraction
نویسنده
چکیده
We prove that edge contractions do not preserve the property that a set of graphs has bounded clique-width.
منابع مشابه
Graph Operations on Clique-Width Bounded Graphs
In this paper we survey the behavior of various graph operations on the graph parameters clique-width and NLC-width. We give upper and lower bounds for the clique-width and NLC-width of the modi ed graphs in terms of the clique-width and NLC-width of the involved graphs. Therefor we consider the binary graph operations join, co-join, sum, di erence, products, corona, substitution, and 1-sum, an...
متن کاملEdge contraction and edge removal on iterated clique graphs
The clique graph K(G) of a graph G is the intersection graph of all its (maximal) cliques. We explore the effect of operations like edge contraction, edge removal and others on the dynamical behaviour of a graph under the iteration of the clique operator K. As a consequence of this study, we can now prove the clique divergence of graphs for which no previously known technique would yield the re...
متن کاملThe enumeration of vertex induced subgraphs with respect to the number of components
Inspired by the study of community structure in connection networks, we introduce the graph polynomial Q (G;x, y), the bivariate generating function which counts the number of connected components in induced subgraphs. We give a recursive definition of Q (G; x, y) using vertex deletion, vertex contraction and deletion of a vertex together with its neighborhood and prove a universality property....
متن کاملIntractability of Clique-Width Parameterizations
We show that Edge Dominating Set, Hamiltonian Cycle, and Graph Coloring are W [1]-hard parameterized by clique-width. It was an open problem, explicitly mentioned in several papers, whether any of these problems is fixed parameter tractable when parameterized by the clique-width, that is, solvable in time g(k) · nO(1) on n-vertex graphs of clique-width k, where g is some function of k only. Our...
متن کاملClique-width: on the price of generality
Many hard problems can be solved efficiently when the input is restricted to graphs of bounded treewidth. By the celebrated result of Courcelle, every decision problem expressible in monadic second order logic is fixed parameter tractable when parameterized by the treewidth of the input graph. Moreover, for every fixed k ≥ 0, such problems can be solved in linear time on graphs of treewidth at ...
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:
- Inf. Process. Lett.
دوره 114 شماره
صفحات -
تاریخ انتشار 2014