منابع مشابه
Algorithmic Aspects of the Generalized Clique-transversal Problem on Chordal Graphs
Suppose G=( V,E) is a graph in which each maximal clique Ci is associated with an integer ri, where 0 < ri < ICi 1. The generalized clique transversal problem is to determine the minimum cardinality of a subset D of V such that ID n Cij >ri for every maximal clique Ci of G. The problem includes the clique-transversal problem, the i, 1 clique-cover problem, and for perfect graphs, the maximum q-...
متن کاملClique Graphs of Chordal and Path Graphs
Clique graphs of chordal and path graphs are characterized. A special class of graphs named expanded trees is discussed. It consists of a subclass of disk-Helly graphs. It is shown that the clique graph of every chordal (hence path) graph is an expanded tree. In addition, every expanded tree is the clique graph of some path (hence chordal) graph. Diierent characterizations of expanded trees are...
متن کاملReduced clique graphs of chordal graphs
We investigate the properties of chordal graphs that follow from the well-known fact that chordal graphs admit tree representations. In particular, we study the structure of reduced clique graphs which are graphs that canonically capture all tree representations of chordal graphs. We propose a novel decomposition of reduced clique graphs based on two operations: edge contraction and removal of ...
متن کاملClique cutsets beyond chordal graphs
Truemper configurations (thetas, pyramids, prisms, and wheels) have played an important role in the study of complex hereditary graph classes (e.g. the class of perfect graphs and the class of even-hole-free graphs), appearing both as excluded configurations, and as configurations around which graphs can be decomposed. In this paper, we study the structure of graphs that contain (as induced sub...
متن کاملChordal Graphs and Their Clique Graphs
In the rst part of this paper, a new structure for chordal graph is introduced, namely the clique graph. This structure is shown to be optimal with regard to the set of clique trees. The greedy aspect of the recognition algorithms of chordal graphs is studied. A new greedy algorithm that generalizes both Maximal cardinality Search (MCS) and Lexicographic Breadth rst search is presented. The tra...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(98)00087-9