کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4650419 | 1342487 | 2008 | 9 صفحه PDF | دانلود رایگان |
![عکس صفحه اول مقاله: The pebbling threshold of the square of cliques The pebbling threshold of the square of cliques](/preview/png/4650419.png)
Given an initial configuration of pebbles on a graph, one can move pebbles in pairs along edges, at the cost of one of the pebbles moved, with the objective of reaching a specified target vertex. The pebbling number of a graph is the minimum number of pebbles so that every configuration of that many pebbles can reach any chosen target. The pebbling threshold of a sequence of graphs is roughly the number of pebbles so that almost every (resp. almost no) configuration of asymptotically more (resp. fewer) pebbles can reach any chosen target. In this paper we find the pebbling threshold of the sequence of squares of cliques, improving upon an earlier result of Boyle and verifying an important instance of a probabilistic version of Graham's product conjecture.
Journal: Discrete Mathematics - Volume 308, Issue 19, 6 October 2008, Pages 4306–4314