{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:20Z","timestamp":1753893800343,"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>For a fixed graph  $H$, a graph  $G$  is  $H$-saturated if there is no copy of $H$ in  $G$, but  for any edge  $e \\notin G$, there is a copy  of  $H$  in  $G + e$.  The collection of $H$-saturated graphs of order  $n$  is  denoted by  ${\\bf SAT}(n,H)$, and the saturation number, ${\\bf sat}(n, H),$ is the minimum number of edges in a graph in ${\\bf SAT}(n,H)$.  Let $T_k$ be a tree on $k$ vertices. The saturation numbers  ${\\bf sat}(n,T_k)$ for some families of trees will be determined precisely. Some classes of trees for which ${\\bf sat}(n, T_k)  &lt;  n$ will be identified, and trees  $T_k$ in which graphs in ${\\bf SAT}(n,T_k)$ are forests will be presented. Also, families of trees for which ${\\bf sat}(n,T_k) \\geq n$  will be presented.  The maximum and minimum values of ${\\bf sat}(n,T_k)$ for the class of all trees will be given.  Some properties of ${\\bf sat}(n,T_k)$ and ${\\bf SAT} (n,T_k)$ for trees will be discussed.<\/jats:p>","DOI":"10.37236\/180","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T23:28:09Z","timestamp":1578698889000},"source":"Crossref","is-referenced-by-count":9,"title":["Saturation Numbers for Trees"],"prefix":"10.37236","volume":"16","author":[{"given":"Jill","family":"Faudree","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ralph J.","family":"Faudree","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ronald J.","family":"Gould","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Michael S.","family":"Jacobson","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"23455","published-online":{"date-parts":[[2009,7,24]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r91\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r91\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T21:50:15Z","timestamp":1579297815000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r91"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,7,24]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/180","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,7,24]]},"article-number":"R91"}}