{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:22Z","timestamp":1753893802558,"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 directed graph, and let $\\Delta^{ACY}_G$ be the simplicial complex whose simplices are the edge sets of acyclic subgraphs of $G$. Similarly, we define $\\Delta^{NSC}_G$ to be the simplicial complex with the edge sets of not strongly connected subgraphs of $G$ as simplices. We show that $\\Delta^{ACY}_G$ is homotopy equivalent to the $(n-1-k)$-dimensional sphere if $G$ is a disjoint union of $k$ strongly connected graphs. Otherwise, it is contractible. If $G$ belongs to a certain class of graphs, the homotopy type of $\\Delta^{NSC}_G$ is shown to be a wedge of $(2n-4)$-dimensional spheres. The number of spheres can easily be read off the chromatic polynomial of a certain associated undirected graph. We also consider some consequences related to finite topologies and hyperplane arrangements.<\/jats:p>","DOI":"10.37236\/1828","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T21:31:32Z","timestamp":1578691892000},"source":"Crossref","is-referenced-by-count":2,"title":["Directed Subgraph Complexes"],"prefix":"10.37236","volume":"11","author":[{"given":"Axel","family":"Hultman","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2004,10,26]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r75\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v11i1r75\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:53:12Z","timestamp":1579305192000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v11i1r75"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2004,10,26]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2004,1,2]]}},"URL":"https:\/\/doi.org\/10.37236\/1828","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2004,10,26]]},"article-number":"R75"}}