Dominating cliques in chordal graphs

D Kratsch, P Damaschke, A Lubiw - Discrete Mathematics, 1994 - Elsevier
Discrete Mathematics, 1994Elsevier
… A strongly chordal graph which has a dominating clique has one as small as the smallest
dominating set-and, … The aim of this paper is to prove that a chordal graph has a
dominating clique iff it has diameter at most 3, and to prove-by means of a linear-time
algorithm-that a strongly chordal graph which has a dominating clique has one as small as
the smallest dominating set. … We need only show that every chordal graph with diameter
no more than 3 has a dominating clique. This can be done by induction on the number n of …
Abstract
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.
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