{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:43Z","timestamp":1753893823366,"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>Recently, attempts were made to generalize the undirected branching greedoid to a greedoid whose feasible sets consist of sets of edges containing the root satisfying additional size restrictions.  Although this definition does not always result in a greedoid, the lift of the undirected branching greedoid has the properties desired by the authors. The $k$-th lift of a greedoid has sets whose nullity is at most $k$ in the original greedoid.  We prove that if the greedoid is $n$-connected, then its lift is also $n$-connected.  Additionally, for any cut-vertex $v$ and cut-edge $e$ of a graph $\\Gamma$, let $C(v)$ be the component of $\\Gamma\\setminus v$ containing the root and $C(e)$ be the component of $\\Gamma\\setminus e$ containing the root. We prove that if the $k$-th lift of the undirected branching greedoid is 2-connected, then $$\\eqalign{ |{E(C(v))}|&amp; &lt; |{V(C(v))}|+k-1\\hbox{ and }\\cr |{E(C(e))}|&amp;&gt;|{E(\\Gamma)}|-{k}-2.\\cr }$$ We also give examples indicating that no sufficient conditions for the $k$th lift to be 2-connected exists similar to these necessary conditions.<\/jats:p>","DOI":"10.37236\/1010","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:50:46Z","timestamp":1578718246000},"source":"Crossref","is-referenced-by-count":0,"title":["Connectivity of the Lifts of a Greedoid"],"prefix":"10.37236","volume":"14","author":[{"given":"Steven J.","family":"Tedford","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2007,5,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1n9\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1n9\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:02:56Z","timestamp":1579320176000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1n9"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,5,23]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/1010","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2007,5,23]]},"article-number":"N9"}}