Clique-width of unit interval graphs
نویسنده
چکیده
The clique-width is known to be unbounded in the class of unit interval graphs. In this paper, we show that this is a minimal hereditary class of unbounded clique-width, i.e., in every hereditary subclass of unit interval graphs the clique-width is bounded by a constant.
منابع مشابه
On the Clique-Width of Perfect Graph Classes
Graphs of clique–width at most k were introduced by Courcelle, Engelfriet and Rozenberg (1993) as graphs which can be defined by k-expressions based on graph operations which use k vertex labels. In this paper we study the clique–width of perfect graph classes. On one hand, we show that every distance–hereditary graph, has clique– width at most 3, and a 3–expression defining it can be obtained ...
متن کاملClique-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 کاملNew representation results for planar graphs
A universal representation theorem is derived that shows any graph is the intersection graph of one chordal graph, a number of co-bipartite graphs, and one unit interval graph. Central to the the result is the notion of the clique cover width which is a generalization of the bandwidth parameter. Specifically, we show that any planar graph is the intersection graph of one chordal graph, four co-...
متن کاملExploiting Restricted Linear Structure to Cope with the Hardness of Clique-Width
Clique-width is an important graph parameter whose computation is NP-hard. In fact we do not know of any other algorithm than brute force for the exact computation of clique-width on any non-trivial graph class. Results so far indicate that proper interval graphs constitute the first interesting graph class on which we might have hope to compute clique-width, or at least its linear variant line...
متن کاملA new representation of proper interval graphs with an application to clique-width
We introduce a new representation of proper interval graphs that can be computed in linear time and stored in O(n) space. This representation is a 2-dimensional vertex partition. It is particularly interesting with respect to clique-width. Based on this representation, we prove new upper bounds on the clique-width of proper interval graphs.
متن کامل