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In this paper, we consider as a model of cohesive subgraph the 2-clubs, which are induced subgraphs of diameter at most 2. We prove new complexity results on the<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathsf {Min~2\\text {-}Club~Cover}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>Min<\/mml:mi><mml:mspace\/><mml:mn>2<\/mml:mn><mml:mtext>-<\/mml:mtext><mml:mi>Club<\/mml:mi><mml:mspace\/><mml:mi>Cover<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>problem, a variant recently introduced in the literature which asks to cover the vertices of a graph with a minimum number of 2-clubs. First, we answer an open question on the decision version of<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathsf {Min~2\\text {-}Club~Cover}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>Min<\/mml:mi><mml:mspace\/><mml:mn>2<\/mml:mn><mml:mtext>-<\/mml:mtext><mml:mi>Club<\/mml:mi><mml:mspace\/><mml:mi>Cover<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>that asks if it is possible to cover a graph with at most two 2-clubs, and we prove that it is W[1]-hard when parameterized by the distance to a 2-club. Then, we consider the complexity of<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathsf {Min~2\\text {-}Club~Cover}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>Min<\/mml:mi><mml:mspace\/><mml:mn>2<\/mml:mn><mml:mtext>-<\/mml:mtext><mml:mi>Club<\/mml:mi><mml:mspace\/><mml:mi>Cover<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>on some graph classes. We prove that<jats:inline-formula><jats:alternatives><jats:tex-math>$$\\mathsf {Min~2\\text {-}Club~Cover}$$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><mml:mrow><mml:mi>Min<\/mml:mi><mml:mspace\/><mml:mn>2<\/mml:mn><mml:mtext>-<\/mml:mtext><mml:mi>Club<\/mml:mi><mml:mspace\/><mml:mi>Cover<\/mml:mi><\/mml:mrow><\/mml:math><\/jats:alternatives><\/jats:inline-formula>remains NP-hard on subcubic planar graphs, W[2]-hard on bipartite graphs when parameterized by the number of 2-clubs in a solution, and fixed-parameter tractable on graphs having bounded treewidth.<\/jats:p>","DOI":"10.1007\/s00453-022-01062-3","type":"journal-article","created":{"date-parts":[[2022,11,21]],"date-time":"2022-11-21T07:05:54Z","timestamp":1669014354000},"page":"992-1028","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["On the Tractability of Covering a Graph with 2-Clubs"],"prefix":"10.1007","volume":"85","author":[{"given":"Riccardo","family":"Dondi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Manuel","family":"Lafond","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,11,21]]},"reference":[{"key":"1062_CR1","doi-asserted-by":"publisher","first-page":"113","DOI":"10.1080\/0022250X.1973.9989826","volume":"3","author":"RD Alba","year":"1973","unstructured":"Alba, R.D.: A graph-theoretic definition of a sociometric clique. 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