NDLI: Clique r-Domination and Clique r-Packing Problems on Dually Chordal Graphs

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Clique r-Domination and Clique r-Packing Problems on Dually Chordal Graphs

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Brandstdt, Andreas Chepoi, Victor D. Dragan, Feodor F.
Copyright Year	1997
Abstract	Let $\cal C$ be a family of cliques of a graph G=(V,E). Suppose that each clique C of $\cal C$ is associated with an integer r(C)$, where $r(C) \ge 0$. A vertex vr-dominates a clique C of G if $d(v,x) \le r(C)$ for all $x \in C$, where d(v,x) is the standard graph distance. A subset $D \subseteq V$ is a clique r-dominating set of G if for every clique $C \in \cal C$ there is a vertex $u \in D$ which r-dominates C. A clique r-packing set is a subset $P \subseteq \cal C$ such that there are no two distinct cliques $C',C'\in P$ r-dominated by a common vertex of G. The clique r-domination problem is to find a clique r-dominating set with minimum size and the clique r-packing problem is to find a clique r-packing set with maximum size. The formulated problems include many domination and clique-transversal-related problems as special cases. In this paper an efficient algorithm is proposed for solving these problems on dually chordal graphswhich are a natural generalization of strongly chordal graphs. The efficient algorithm is mainly based on the tree structure and special vertex elimination orderings of dually chordal graphs. In some important particular cases where the algorithm works in linear time the obtained results generalize and improve known results on strongly chordal graphs.
Starting Page	109
Ending Page	127
Page Count	19
File Format	PDF
ISSN	08954801
DOI	10.1137/S0895480194267853
e-ISSN	10957146
Journal	SIAM Journal on Discrete Mathematics (SJDMEC)
Issue Number	1
Volume Number	10
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-08-01
Access Restriction	Subscribed
Subject Keyword	dually chordal graphs covering and packing problems tree structure Graph theory hypertrees graphs Analysis of algorithms and problem complexity Factorization, matching, partitioning, covering and packing hypergraphs transversal and matching problems clique hypergraphs Hypergraphs generalization of strongly chordal graphs
Content Type	Text
Resource Type	Article
Subject	Mathematics

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