Dominating sets for split and bipartite graphs
Information Processing Letters
SIAM Journal on Discrete Mathematics
Graph classes: a survey
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
A linear time recognition algorithm for proper interval graphs
Information Processing Letters
On the complexity of signed and minus total domination in graphs
Information Processing Letters
Journal of Computer and System Sciences
Information Processing Letters
Algorithmic aspects of k-tuple total domination in graphs
Information Processing Letters
Hi-index | 0.89 |
For a graph G=(V,E), a dominating set is a set D@?V such that every vertex v@?V@?D has a neighbor in D. Given a graph G=(V,E) and a positive integer k, the minimum outer-connected dominating set problem for G is to decide whether G has a dominating set D of cardinality at most k such that G[V@?D], the induced subgraph by G on V@?D, is connected. In this paper, we consider the complexity of the minimum outer-connected dominating set problem for the class of chordal graphs. In particular, we show that the minimum outer-connected dominating set problem is NP-complete for doubly chordal graphs and undirected path graphs, two well studied subclasses of chordal graphs. We also give a linear time algorithm for computing a minimum outer-connected dominating set in proper interval graphs. Notice that proper interval graphs form a subclass of undirected path graphs as well as doubly chordal graphs.