{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:47:08Z","timestamp":1759063628352,"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 $G = (V,E)$ be a graph and $k \\ge 0$ an integer. A $k$-independent set $S \\subseteq V$ is a set of vertices such that the maximum degree in the graph induced by $S$ is at most $k$. With $\\alpha_k(G)$ we denote the maximum cardinality of a $k$-independent set of $G$. We prove that, for a graph $G$ on $n$ vertices and average degree $d$, $\\alpha_k(G) \\ge \\frac{k+1}{\\lceil d \\rceil + k + 1} n$, improving the hitherto best general lower bound due to Caro and Tuza [Improved lower bounds on $k$-independence, J. Graph Theory 15 (1991), 99-107].<\/jats:p>","DOI":"10.37236\/2646","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T02:58:57Z","timestamp":1578711537000},"source":"Crossref","is-referenced-by-count":19,"title":["New Approach to the $k$-Independence Number of a Graph"],"prefix":"10.37236","volume":"20","author":[{"given":"Yair","family":"Caro","sequence":"first","affiliation":[]},{"given":"Adriana","family":"Hansberg","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2013,2,12]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p33\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v20i1p33\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T11:27:03Z","timestamp":1579260423000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v20i1p33"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,2,12]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2013,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/2646","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2013,2,12]]},"article-number":"P33"}}