Neighborhood inclusions for minimal dominating sets enumeration: linear and polynomial delay algorithms in P_7-free and P_8-free chordal graphs [article]

Oscar Defrain, Lhouari Nourine
2019 arXiv   pre-print
In [M. M. Kanté, V. Limouzy, A. Mary, and L. Nourine. On the enumeration of minimal dominating sets and related notions. SIAM Journal on Discrete Mathematics, 28(4):1916-1929, 2014] the authors give an O(n+m) delay algorithm based on neighborhood inclusions for the enumeration of minimal dominating sets in split and P_6-free chordal graphs. In this paper, we investigate generalizations of this technique to P_k-free chordal graphs for larger integers k. In particular, we give O(n+m) and O(n^3·
more » ... delays algorithms in the classes of P_7-free and P_8-free chordal graphs. As for P_k-free chordal graphs for k≥ 9, we give evidence that such a technique is inefficient as a key step of the algorithm, namely the irredundant extension problem, becomes NP-complete.
arXiv:1805.02412v2 fatcat:yvlfpi42snbahgvcuoukzgdmj4