{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:45Z","timestamp":1753893825825,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $G$ be a graph on the vertex set $V$. A vertex subset $W \\subseteq V$ is a\u00a0cover\u00a0of $G$ if $V \\setminus W$ is an independent set of $G$, and $W$ is a non-cover\u00a0of $G$ if $W$ is not a cover of $G$. The\u00a0non-cover complex\u00a0of $G$ is a simplicial complex on $V$ whose faces are non-covers of $G$. Then the non-cover complex of $G$ is the combinatorial Alexander dual of the independence complex of $G$. Aharoni asked if the non-cover complex of a graph $G$ without isolated vertices is $(|V(G)|-i\\gamma(G)-1)$-collapsible where $i\\gamma(G)$ denotes the independence domination number of $G$. Extending a result by the second author, who verified Aharoni's question in the affirmative for chordal graphs, we prove that the answer to the question is yes for all graphs.<\/jats:p>","DOI":"10.37236\/8684","type":"journal-article","created":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T09:18:27Z","timestamp":1579857507000},"source":"Crossref","is-referenced-by-count":1,"title":["Collapsibility of Non-Cover Complexes of Graphs"],"prefix":"10.37236","volume":"27","author":[{"given":"Ilkyoo","family":"Choi","sequence":"first","affiliation":[]},{"given":"Jinha","family":"Kim","sequence":"additional","affiliation":[]},{"given":"Boram","family":"Park","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2020,1,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p20\/8005","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v27i1p20\/8005","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,24]],"date-time":"2020-01-24T09:18:27Z","timestamp":1579857507000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v27i1p20"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,1,24]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2020,1,9]]}},"URL":"https:\/\/doi.org\/10.37236\/8684","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2020,1,24]]},"article-number":"P1.20"}}