Clique Graphs of Chordal and Path Graphs
نویسندگان
چکیده
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 described, leading to a polynomial time algorithm for recognizing them.
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 کاملEnumeration of P 4-Free Chordal Graphs
We count labelled chordal graphs with no induced path of length 3, both exactly and asymptotically. These graphs correspond to rooted trees in which no vertex has exactly one child, and each vertex has been expanded to a clique. Some properties of random graphs of this type are also derived. The corresponding unlabelled graphs are in 1-1 correspondence with unlabelled rooted trees on the same n...
متن کاملFinding intersection models: From chordal to Helly circular-arc graphs
Every chordal graph G admits a representation as the intersection graph of a family of subtrees of a tree. A classic way of finding such an intersection model is to look for a maximum spanning tree of the valuated clique graph of G. Similar techniques have been applied to find intersection models of chordal graph subclasses as interval graphs and path graphs. In this work, we extend those metho...
متن کاملOn basic chordal graphs and some of its subclasses
Basic chordal graphs arose when comparing clique trees of chordal graphs and compatible trees of dually chordal graphs. They were defined as those chordal graphs whose clique trees are exactly the compatible trees of its clique graph. In this work, we consider some subclasses of basic chordal graphs. One of them is the class of hereditary basic chordal graphs, which will turn out to have many p...
متن کاملAn Approach to Hadwiger's Conjecture through Squares of Chordal Graphs
Hadwiger’s conjecture states that for every graph G, χ(G) ≤ η(G), where χ(G) is the chromatic number and η(G) is the size of the largest clique minor in G. In this work, we show that to prove Hadwiger’s conjecture in general, it is sufficient to prove Hadwiger’s conjecture for the class of graphs F defined as follows: F is the set of all graphs that can be expressed as the square graph of a spl...
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:
- SIAM J. Discrete Math.
دوره 7 شماره
صفحات -
تاریخ انتشار 1994