{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:50Z","timestamp":1753893830591,"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>In graph pebbling games, one considers a distribution of pebbles on the vertices of a graph, and a pebbling move consists of taking two pebbles off one vertex and  placing one on an adjacent vertex.  The $t$-pebbling number $\\pi_t(G)$ of a graph $G$ is the smallest $m$ such that for every initial distribution of $m$ pebbles  on $V(G)$ and every target vertex $x$ there exists a sequence of pebbling moves leading to a distibution with at least $t$ pebbles at $x$. Answering a question of Sieben, we show that for every graph $G$, $\\pi_t(G)$ is eventually linear in $t$; that is, there are numbers $a,b,t_0$ such that $\\pi_t(G)=at+b$ for all $t\\ge t_0$. Our result is also valid for weighted graphs, where every edge $e=\\{u,v\\}$ has some integer weight $\\omega(e)\\ge 2$, and a pebbling move from $u$ to $v$ removes $\\omega(e)$ pebbles at $u$ and adds one pebble to $v$.<\/jats:p>","DOI":"10.37236\/640","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:43:40Z","timestamp":1578714220000},"source":"Crossref","is-referenced-by-count":1,"title":["The $t$-Pebbling Number is Eventually Linear in $t$"],"prefix":"10.37236","volume":"18","author":[{"given":"Michael","family":"Hoffmann","sequence":"first","affiliation":[]},{"given":"Ji\u0159\u00ed","family":"Matou\u0161ek","sequence":"additional","affiliation":[]},{"given":"Yoshio","family":"Okamoto","sequence":"additional","affiliation":[]},{"given":"Philipp","family":"Zumstein","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2011,7,22]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p153\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p153\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:07:43Z","timestamp":1579302463000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p153"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,7,22]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/640","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,7,22]]},"article-number":"P153"}}