TY - JOUR

T1 - Clustering and domination in perfect graphs

AU - Corneil, D. G.

AU - Perl, Y.

N1 - Funding Information:
The authors wish to thank the Natural Sciences and Engineering Research Council of Canada for financial assistance. We also wish to thank Martin Farber for the use of his proof of Theorem 4.1 and both Martin Farber and Mark Keil for their comments on the domination problem.

PY - 1984/9

Y1 - 1984/9

N2 - A k-cluster in a graph is an induced subgraph on k vertices which maximizes the number of edges. Both the k-cluster problem and the k-dominating set problem are NP-complete for graphs in general. In this paper we investigate the complexity status of these problems on various sub-classes of perfect graphs. In particular, we examine comparability graphs, chordal graphs, bipartite graphs, split graphs, cographs and κ-trees. For example, it is shown that the k-cluster problem is NP-complete for both bipartite and chordal graphs and the independent k-dominating set problem is NP-complete for bipartite graphs. Furthermore, where the k-cluster problem is polynomial we study the weighted and connected versions as well. Similarly we also look at the minimum k-dominating set problem on families which have polynomial k-dominating set algorithms.

AB - A k-cluster in a graph is an induced subgraph on k vertices which maximizes the number of edges. Both the k-cluster problem and the k-dominating set problem are NP-complete for graphs in general. In this paper we investigate the complexity status of these problems on various sub-classes of perfect graphs. In particular, we examine comparability graphs, chordal graphs, bipartite graphs, split graphs, cographs and κ-trees. For example, it is shown that the k-cluster problem is NP-complete for both bipartite and chordal graphs and the independent k-dominating set problem is NP-complete for bipartite graphs. Furthermore, where the k-cluster problem is polynomial we study the weighted and connected versions as well. Similarly we also look at the minimum k-dominating set problem on families which have polynomial k-dominating set algorithms.

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U2 - 10.1016/0166-218X(84)90088-X

DO - 10.1016/0166-218X(84)90088-X

M3 - Article

AN - SCOPUS:0021483662

VL - 9

SP - 27

EP - 39

JO - Discrete Applied Mathematics

JF - Discrete Applied Mathematics

SN - 0166-218X

IS - 1

ER -