dc.contributor.author | Emmanuel, Sam | |
dc.contributor.author | Fellows, Michael Ralph | |
dc.contributor.author | Rosamond, Frances | |
dc.contributor.author | Golovach, Petr | |
dc.date.accessioned | 2024-08-14T09:20:12Z | |
dc.date.available | 2024-08-14T09:20:12Z | |
dc.date.created | 2024-01-16T12:58:09Z | |
dc.date.issued | 2023 | |
dc.identifier.issn | 0302-9743 | |
dc.identifier.uri | https://hdl.handle.net/11250/3146239 | |
dc.description.abstract | A lineal topology T = (G, r, T ) of a graph G is an r-rooted depth-first spanning (DFS) tree T of G. Equivalently, this is a spanning tree of G such that every edge uv of G is either an edge of T or is between a vertex u and an ancestor v on the unique path in T from u to r. We consider the parameterized complexity of finding a lineal topology that satisfies upper or lower bounds on the number of leaves of T , parameterized by the bound. This immediately yields four natural parameterized problems: (i) ≤ k leaves, (ii) ≥ k leaves, (iii) ≤ n − k leaves, and (iv) ≥ n − k leaves, where n = |G|. We show that all four problems are NP-hard, considered classically. We show that (i) is para- NP-hard, (ii) is hard for W[1], (iii) is FPT, and (iv) is FPT. Our work is motivated by possible applications in graph drawing and visualization. | en_US |
dc.language.iso | eng | en_US |
dc.publisher | Springer | en_US |
dc.title | On the Parameterized Complexity of the Structure of Lineal Topologies (Depth-First Spanning Trees) of Finite Graphs: The Number of Leaves | en_US |
dc.type | Journal article | en_US |
dc.type | Peer reviewed | en_US |
dc.description.version | acceptedVersion | en_US |
cristin.ispublished | true | |
cristin.fulltext | postprint | |
cristin.qualitycode | 1 | |
dc.identifier.doi | https://doi.org/10.1007/978-3-031-30448-4_25 | |
dc.identifier.cristin | 2227687 | |
dc.source.journal | Lecture Notes in Computer Science (LNCS) | en_US |
dc.source.pagenumber | 353-367 | en_US |
dc.relation.project | Norges forskningsråd: 314528 | en_US |
dc.identifier.citation | Lecture Notes in Computer Science (LNCS). 2023, 13898, 353-367. | en_US |
dc.source.volume | 13898 | en_US |