{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:25Z","timestamp":1753893865786,"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>The combinatorial  Alexander dual  of the independence complex $\\mathrm{Ind}(G)$ and that of the edge covering complex $\\mathrm{EC}(G)$ are shown to have isomorphic homology groups for each non-null graph $G$.  This yields isomorphisms of homology groups of $\\mathrm{Ind}(G)$ and $\\mathrm{EC}(G)$ with homology dimensions being appropriately shifted and restricted.  The results exhibits the complementary nature of homology groups of $\\mathrm{Ind}(G)$ and $\\mathrm{EC}(G)$ which had been proved by Ehrenborg-Hetyei, Engstr\u00f6m, and Marietti-Testa for forests at homotopy level.<\/jats:p>","DOI":"10.37236\/526","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:53:25Z","timestamp":1578714805000},"source":"Crossref","is-referenced-by-count":1,"title":["Independence Complexes and Edge Covering Complexes via Alexander Duality"],"prefix":"10.37236","volume":"18","author":[{"given":"Kazuhiro","family":"Kawamura","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2011,2,14]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p39\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p39\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:16:24Z","timestamp":1579302984000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p39"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,2,14]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/526","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,2,14]]},"article-number":"P39"}}