✦ LIBER ✦

Dominating cliques in chordal graphs

✍ Scribed by Dieter Kratsch; Peter Damaschke; Anna Lubiw

Publisher: Elsevier Science
Year: 1994
Tongue: English
Weight: 492 KB
Volume: 128
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(94)90118-x

No coin nor oath required. For personal study only.

✦ Synopsis

A chordal graph has a dominating clique iff it has diameter at most 3. A strongly chordal graph which has a dominating clique has one as small as the smallest dominating set-and, furthermore, there is a linear-time algorithm to find such a small dominating clique.

📜 SIMILAR VOLUMES

Finding dominating cliques efficiently,

Finding dominating cliques efficiently, in strongly chordal graphs and undirected path graphs

✍ Dieter Kratsch 📂 Article 📅 1990 🏛 Elsevier Science 🌐 English ⚖ 914 KB

We study a new version of the domination problem in which the dominating set is required to be a clique. The minimum dominating clique problem is NP-complete for split graphs and, hence, for chordal graphs. We show that for two other important subclasses of chordal graphs the problem is solvable eff

Squares, clique graphs, and chordality

✍ W. D. Wallis; Julin Wu 📂 Article 📅 1995 🏛 John Wiley and Sons 🌐 English ⚖ 427 KB

## Abstract We study the squares and the clique graphs of chordal graphs and various special classes of chordal graphs. Chordality conditions for squares and clique graphs are given. Several theorems concering chordal graphs are generalized. © 1996 John Wiley & Sons, Inc.

r-Dominating cliques in graphs with hype

r-Dominating cliques in graphs with hypertree structure

✍ Feodor F. Dragan; Andreas Brandstädt 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 848 KB

Let G = (V, E) be an undirected graph and r be a vertex weight function with positive integer values. A subset (clique) D ~\_ V is an r-dominating set (clique) in G ifffor every vertex v e V there is a vertex u e D with dist(u, v) <~ r(v). This paper contains the following results: (i) We give a si

Diameters of iterated clique graphs of c

Diameters of iterated clique graphs of chordal graphs

✍ Bor-Liang Chen; Ko-Wei Lih 📂 Article 📅 1990 🏛 John Wiley and Sons 🌐 English ⚖ 272 KB

## Abstract The clique graph __K__(__G__) of a graph is the intersection graph of maximal cliques of __G.__ The iterated clique graph __K__^__n__^(__G__) is inductively defined as __K__(K^n−1^(__G__)) and __K__^1^(__G__) = __K__(__G__). Let the diameter diam(__G__) be the greatest distance between

On covering all cliques of a chordal gra

On covering all cliques of a chordal graph

✍ Thomas Andreae; Carsten Flotow 📂 Article 📅 1996 🏛 Elsevier Science 🌐 English ⚖ 205 KB

For a graph G = (V,E), a vertex set XC\_ V is called a clique if Ixl>~2 and the graph G [X] induced by X is a complete subgraph maximal under inclusion. We say that a vertex set T is a clique-transversal set if T N X ~ 0 for all cliques X of G, and define the clique-transversal number re(G) as the m

Strong clique trees, neighborhood trees,

Strong clique trees, neighborhood trees, and strongly chordal graphs

✍ McKee, Terry A. 📂 Article 📅 2000 🏛 John Wiley and Sons 🌐 English ⚖ 137 KB 👁 1 views

Maximal complete subgraphs and clique trees are basic to both the theory and applications of chordal graphs. A simple notion of strong clique tree extends this structure to strongly chordal graphs. Replacing maximal complete subgraphs with open or closed vertex neighborhoods discloses new relationsh