Name
Abstract | ||
|---|---|---|
Let G be a connected graph. A configuration of pebbles assigns a nonnegative integer number of pebbles to each vertex of G. A move consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. A configuration is solvable if any vertex can get at least one pebble through a sequence of moves. The pebbling number of G, denoted π(G), is the smallest integer such that any configuration of π(G) pebbles on G is solvable. A graph has the two-pebbling property if after placing more than 2π(G)−q pebbles on G, where q is the number of vertices with pebbles, there is a sequence of moves so that at least two pebbles can be placed on any vertex. A graph has the odd-two-pebbling property if after placing more than 2π(G)−r pebbles on G, where r is the number of vertices with an odd number of pebbles, there is a sequence of moves so that at least two pebbles can be placed on any vertex. In this paper, we prove that the two-pebbling and odd-two-pebbling properties are not equivalent. |
Year | DOI | Venue |
|---|---|---|
2019 | 10.1016/j.disc.2018.10.030 | Discrete Mathematics |
Keywords | Field | DocType |
Graph pebbling,Lemke graph,Two-pebbling,Odd-two-pebbling | Integer,Graph,Discrete mathematics,Combinatorics,Vertex (geometry),Neighbourhood (graph theory),Pebble,Connectivity,Mathematics | Journal |
Volume | Issue | ISSN |
342 | 3 | 0012-365X |
Citations | PageRank | References |
0 | 0.34 | 5 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Charles A. Cusack | 1 | 22 | 4.89 |
| Airat Bekmetjev | 2 | 24 | 3.71 |
| Mark Powers | 3 | 1 | 1.07 |