2026-07-23T03:56:16Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:13364 2024-03-06T10:51:47Z ddc:004 open_access

Computing Dense and Sparse Subgraphs of Weakly Closed Graphs Koana, Tomohiro Komusiewicz, Christian Sommer, Frank Fixed-parameter tractability c-closure degeneracy clique relaxations bicliques dominating set A graph G is weakly γ-closed if every induced subgraph of G contains one vertex v such that for each non-neighbor u of v it holds that |N(u)∩ N(v)| < γ. The weak closure γ(G) of a graph, recently introduced by Fox et al. [SIAM J. Comp. 2020], is the smallest number such that G is weakly γ-closed. This graph parameter is never larger than the degeneracy (plus one) and can be significantly smaller. Extending the work of Fox et al. [SIAM J. Comp. 2020] on clique enumeration, we show that several problems related to finding dense subgraphs, such as the enumeration of bicliques and s-plexes, are fixed-parameter tractable with respect to γ(G). Moreover, we show that the problem of determining whether a weakly γ-closed graph G has a subgraph on at least k vertices that belongs to a graph class 𝒢 which is closed under taking subgraphs admits a kernel with at most γ k² vertices. Finally, we provide fixed-parameter algorithms for Independent Dominating Set and Dominating Clique when parameterized by γ+k where k is the solution size. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Tomohiro Koana and Christian Komusiewicz and Frank Sommer 2020 Is Part Of LIPIcs, Volume 181, 31st International Symposium on Algorithms and Computation (ISAAC 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ISAAC.2020.20 urn:nbn:de:0030-drops-133646 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2020.20 eng https://creativecommons.org/licenses/by/3.0/legalcode