The Complexity of Pebbling and Cover Pebbling
نویسنده
چکیده
This paper discusses the complexity of graph pebbling, dealing with both traditional pebbling and the recently introduced game of cover pebbling. Determining whether a configuration is solvable according to either the traditional definition or the cover pebbling definition is shown to be NP -complete. The problem of determining the cover pebbling number for an arbitrary demand configuration is shown to be NP -hard. 1
منابع مشابه
Threshold and complexity results for the cover pebbling game
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, γ(G), is the smallest number of pebbles such that through a sequence of pebbling moves, a pebble can eventually be placed on every vertex simultaneously, no matter how the pebbles are ...
متن کاملDomination Cover Pebbling: Structural Results
This paper continues the results of “Domination Cover Pebbling: Graph Families.” An almost sharp bound for the domination cover pebbling (DCP) number, ψ(G), for graphs G with specified diameter has been computed. For graphs of diameter two, a bound for the ratio between λ(G), the cover pebbling number of G, and ψ(G) has been computed. A variant of domination cover pebbling, called subversion DC...
متن کاملThe Cover Pebbling Theorem
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 cover pebbling starting with all pebbles on one node is trivial to compute and it was conjectured that the maximum of these simple cover pebbling numbers is...
متن کاملDomination Cover Pebbling: Graph Families
Given a configuration of pebbles on the vertices of a connected graph G, a pebbling move is defined as the removal of two pebbles from some vertex, and the placement of one of these on an adjacent vertex. We introduce the notion of domination cover pebbling, obtained by combining graph cover pebbling ([2]) with the theory of domination in graphs ([3]). The domination cover pebbling number, ψ(G)...
متن کاملCover Pebbling Numbers and Bounds for Certain Families of Graphs
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, γ(G), is the smallest number of pebbles such that through a sequence of pebbling moves, a pebble can eventually be placed on every vertex simultaneously, no matter how the pebbles are ...
متن کامل