The t-pebbling number is eventually linear in t

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F11%3A10100317" target="_blank" >RIV/00216208:11320/11:10100317 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
The t-pebbling number is eventually linear in t
Original language description
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 graphG, 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 }= t_0. Our result is also valid for weighted graphs, where every edge e={u,v} has some integer weight omega(e)}= 2, and a pebbling move from uto v removes omega(e) pebbles at u and adds one pebble to v.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BD - Information theory
OECD FORD branch
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Project
<a href="/en/project/1M0545" target="_blank" >1M0545: Institute for Theoretical Computer Science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year
2011
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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