Abstract A pebble distribution places a nonnegative number of pebbles on the vertices of a graph G . In graph rubbling, the pebbles can be redistributed using pebbling and rubbling moves, typically with the goal of reaching some target pebble distribution. In graph pebbling, only the pebbling move is allowed. The cover pebbling number is the smallest k such that from any initial distribution of k pebbles, it is possible that after a series of pebbling moves there is at least one pebble on every vertex of G . The Cover Pebbling Theorem asserts that to determine the cover pebbling number of a graph, it is sufficient to consider the pebbling distributions that initially place all pebbles on a single vertex. In this paper, we prove a rubbling analogue of the Cover Pebbling Theorem, providing an answer to an open question of Belford and Sieben (2009). In addition, we prove a stronger version of the Cover Rubbling Theorem for trees.

中文翻译：

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盖板乱码堆放

摘要 鹅卵石分布将非负数量的鹅卵石放置在图 G 的顶点上。在图 rubbling 中，可以使用 pebbling 和 rubbling 移动重新分配鹅卵石，通常以达到某个目标鹅卵石分布为目标。在图形鹅卵石中，只允许鹅卵石移动。覆盖鹅卵石数量是最小的 k ，使得从 k 个鹅卵石的任何初始分布中，有可能在一系列鹅卵石移动之后，在 G 的每个顶点上至少有一个鹅卵石。Cover Pebbling Theorem 断言，要确定图的 Cover Pebbling 数，考虑最初将所有鹅卵石放在单个顶点上的鹅卵石分布就足够了。在本文中，我们证明了 Cover Pebbling Theorem 的 rubbling 模拟，为 Belford 和 Sieben (2009) 的一个悬而未决的问题提供了答案。