Minimum Maximal Acyclic Matching in Proper Interval Graphs

Chaudhary, Juhi; Mishra, Sambit Kumar; Panda, B. S.

doi:10.1007/978-3-031-25211-2_29

Cited by 1 publication

(1 citation statement)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As mentioned, Max Min FVS is an example of a wider class of MaxMin problems which have recently attracted much attention in the literature, among the most well-studied of which are Maximum Minimal Vertex Cover [10,11,33] and Upper Dominating Set (which is the standard name for Maximum Minimal Dominating Set) [1,4,20]. Additionally, MaxMin or MinMax versions of cut and separations problems [18,25,29], knapsack problems [21,23], matching problems [13], and coloring problems [5] have also been studied.…”

Section: Introductionmentioning

confidence: 99%

Parameterized Max Min Feedback Vertex Set

Lampis¹,

Melissinos²,

Vasilakis³

2023

Preprint

View full text Add to dashboard Cite

Given a graph G and an integer k, Max Min FVS asks whether there exists a minimal set of vertices of size at least k whose deletion destroys all cycles. We present several results that improve upon the state of the art of the parameterized complexity of this problem with respect to both structural and natural parameters. Using standard DP techniques, we first present an algorithm of time tw O(tw) n O(1) , significantly generalizing a recent algorithm of Gaikwad et al. of time vc O(vc) n O(1) , where tw, vc denote the input graph's treewidth and vertex cover respectively. Subsequently, we show that both of these algorithms are essentially optimal, since a vc o(vc) n O(1) algorithm would refute the ETH. With respect to the natural parameter k, the aforementioned recent work by Gaikwad et al. claimed an FPT branching algorithm with complexity 10 k n O(1) . We point out that this algorithm is incorrect and present a branching algorithm of complexity 9.34 k n O(1) .

show abstract