Related papers: Pebbling on Directed Graphs with Fixed Diameter
A pebbling move on a graph G consists of the removal of two pebbles from one vertex and the placement of one pebble on an adjacent vertex. Rubbling is a version of pebbling where an additional move is allowed, which is also called the…
Given a configuration of indistinguishable pebbles on the vertices of a graph, a pebbling move consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The pebbling number of a graph is the least…
In a graph G with a distribution of pebbles on its vertices, a pebbling move is the removal of two pebbles from one vertex and the addition of one pebble to an adjacent vertex. A weight function on G is a non-negative integer-valued…
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…
Graph pebbling is a network model for transporting discrete resources that are consumed in transit. Deciding whether a given configuration on a particular graph can reach a specified target is ${\sf NP}$-complete, even for diameter two…
A configuration of pebbles on the vertices of a graph is solvable if one can place a pebble on any given root vertex via a sequence of pebbling steps. A function is a pebbling threshold for a sequence of graphs if a randomly chosen…
In this paper, we define a new parameter of a graph as a spin-off of the pebbling number (which is the smallest $t$ such that every supply of $t$ pebbles can satisfy every demand of one pebble). This new parameter is the singular pebbling…
Suppose that pebbles are distributed on the vertices of a graph G. A pebbling step along an edge uv removes two pebbles from u and places one pebble on v. We introduce two new graph parameters: stack(G): the least integer t such that every…
We explore the complexity of computing the optimal pebbling number and pebbling number of a graph. We show that deciding whether the optimal pebbling number of G is at most k is NP-complete and deciding whether the pebbling number of G is…
Graph pebbling considers the problem of transforming configurations of discrete pebbles to certain target configurations on the vertices of a graph, using the so-called pebbling move. This paper provides counterexamples to a monotonicity…
Given a configuration of pebbles on the vertices of a graph, a pebbling move is defined by removing two pebbles from some vertex and placing one pebble on an adjacent vertex. The cover pebbling number of a graph is the smallest number of…
The pebbling number of a graph $G$, $f(G)$, is the least $p$ such that, however $p$ pebbles are placed on the vertices of $G$, we can move a pebble to any vertex by a sequence of moves, each move taking two pebbles off one vertex and…
For any configuration of pebbles on the nodes of a graph, a pebbling move replaces two pebbles on one node by one pebble on an adjacent node. A cover pebbling is a move sequence ending with no empty nodes. The number of pebbles needed for a…
Let $G$ be a connected graph. A pebbling move is defined as taking two pebbles from one vertex and placing one pebble to an adjacent vertex and throwing away the other pebble. The non-split domination cover pebbling number, $\psi_{ns}(G)$,…
A pebbling move on a graph consists of taking two pebbles off from one vertex and add one pebble on an adjacent vertex, the $t$-pebbling number of a graph $G$ is the minimum number of pebbles so that we can move $t$ pebbles on any vertex on…
A pebbling step on a graph consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. A graph is said to be cover pebbled if every vertex has a pebble on it after a series of pebbling steps. The cover…
Distributions of pebbles to the vertices of a graph are said to be solvable when a pebble may be moved to any specified vertex using a sequence of admissible pebbling rules. The optimal pebbling number is the least number of pebbles needed…
Graph Pebbling is a well-studied single-player game on graphs. We introduce the game of Blocking Pebbles which adapts Graph Pebbling into a two-player strategy game in order to examine it within the context of Combinatorial Game Theory.…
In graph pegging, we view each vertex of a graph as a hole into which a peg can be placed, with checker-like ``pegging moves'' allowed. Motivated by well-studied questions in graph pebbling, we introduce two pegging quantities. The pegging…
Graph pebbling is a problem in which pebbles are distributed across the vertices of a graph and moved according to a specific rule: two pebbles are removed from a vertex to place one on an adjacent vertex. The goal is to determine the…