# Random Ramblings on Graph Pebbling

## Document Type

Presentation Abstract

## Presentation Date

11-18-1999

## Abstract

Given a connected graph *G*, and a distribution of pebbles to the vertices of *G*, a pebbling step consists of removing 2 pebbles from a vertex *v* and placing one pebble on a neighbor of *v*. The “lost pebble” could represent the cost of a computation. For a particular root vertex *r*, the distribution is *r-solvable* if it is possible to place a pebble on *r* after a finite number of pebbling steps. The distribution is *solvable* if it is *r*-solvable for every* **r*. The pebbling number *f(G)* is the least integer *t *so that every distribution of *t* pebbles onto the vertices of *G* is solvable. Thus, starting with *f(G)* pebbles --- even if placed by the devil --- guarantees solvability. What if we place the pebbles at random and ask only for an almost sure guarantee? This introductory talk will explore these ideas and questions, revealing their connections with familiar mathematical ideas.

## Recommended Citation

Kayll, Professor Mark, "Random Ramblings on Graph Pebbling" (1999). *Colloquia of the Department of Mathematical Sciences*. 53.

https://scholarworks.umt.edu/mathcolloquia/53

## Additional Details

Thursday, 18 November 1999

4:10 p.m. in Math 109

Coffee/treats at 3:30 p.m. Math 104 (lounge)