منابع مشابه
On P4-transversals of chordal graphs
A P4-transversal of a graph G is a set of vertices T which meets every P4 of G. A P4transversal T is called stable if there are no edges in the subgraph of G induced by T . It has been previously shown by Hoàng and Le that it is NP -complete to decide whether a comparability (and hence perfect) graph G has a stable P4-transversal. In the following we show that the problem is NP -complete for ch...
متن کاملThe P4-structure of perfect graphs
One of the most important outstanding open problems in algorithmic graph theory is to determine the complexity of recognizing perfect graphs. Results of Lovász [33], Padberg [37] and Bland et al. [6] imply, as was first observed by Cameron [10] in 1982, that the problem of recognizing perfect graphs is in co-NP. So far it is not known whether this problem also belongs to NP, i.e., we do not kno...
متن کاملPerfect graphs with unique P4-structure
We will extend Reed's Semi-Strong Perfect Graph Theorem by proving that unbreakable C 5-free graphs diierent from a C 6 and its complement have unique P 4-structure.
متن کاملOn the P4-structure of perfect graphs I. Even decompositions
Claude Berge proposed to call a graph perfect if, for each of its induced subgraphs F, the chromatic number of F equals the largest number of pairwise adjacent vertices in F. No polynomial-time algorithm for recognizing perfect graphs is known. It is conceivable that such an algorithm would rely on decompositions of all perfect graphs into some “primitive” perfect graphs recognizable in a polyn...
متن کاملOn P4-tidy graphs
We study the P4-tidy graphs, a new class defined by Rusu [30] in order to illustrate the notion of P4-domination in perfect graphs. This class strictly contains the P4-extendible graphs and the P4-lite graphs defined by Jamison & Olariu in [19] and [23] and we show that the P4-tidy graphs and P4-lite graphs are closely related. Note that the class of P4-lite graphs is a class of brittle graphs ...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2000
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(99)00300-3