The domatic number problem on some perfect graph families
Information Processing Letters
Graph classes: a survey
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
Algorithmic Graph Theory and Perfect Graphs (Annals of Discrete Mathematics, Vol 57)
On the Minimum Feedback Vertex Set Problem: Exact and Enumeration Algorithms
Algorithmica - Parameterized and Exact Algorithms
Combinatorial bounds via measure and conquer: Bounding minimal dominating sets and applications
ACM Transactions on Algorithms (TALG)
Feedback vertex sets in tournaments
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Exact Exponential Algorithms
Enumeration of minimal dominating sets and variants
FCT'11 Proceedings of the 18th international conference on Fundamentals of computation theory
Trees having many minimal dominating sets
Information Processing Letters
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The maximum number of minimal dominating sets that a graph on n vertices can have is known to be at most 1.7159n . This upper bound might not be tight, since no examples of graphs with 1.5705n or more minimal dominating sets are known. For several classes of graphs, we substantially improve the upper bound on the maximum number of minimal dominating sets in graphs on n vertices. In some cases, we provide examples of graphs whose number of minimal dominating sets exactly matches the proved upper bound for that class, thereby showing that these bounds are tight. For all considered graph classes, the upper bound proofs are constructive and can easily be transformed into algorithms enumerating all minimal dominating sets of the input graph.