Cops and robbers pebbling in graphs
Nancy Clarke, Joshua Forkin, and Glenn Hurlbert

TL;DR
This paper introduces Cops and Robbers Pebbling, a new graph theory paradigm combining elements of Cops and Robbers and Graph Pebbling, analyzing cop pebbling numbers across various graph classes and exploring related conjectures.
Contribution
It defines the cop pebbling number, provides bounds and exact values for different graphs, and investigates conjectures related to cop pebbling and existing graph theory problems.
Findings
Upper and lower bounds for cop pebbling numbers on various graphs
Exact cop pebbling numbers for specific graph classes
Failure of Graham's Pebbling Conjecture inequality in cop pebbling
Abstract
Here we merge the two fields of Cops and Robbers and Graph Pebbling to introduce the new topic of Cops and Robbers Pebbling. Both paradigms can be described by moving tokens (the cops) along the edges of a graph to capture a special token (the robber). In Cops and Robbers, all tokens move freely, whereas, in Graph Pebbling, some of the chasing tokens disappear with movement while the robber is stationary. In Cops and Robbers Pebbling, some of the chasing tokens (cops) disappear with movement, while the robber moves freely. We define the cop pebbling number of a graph to be the minimum number of cops necessary to capture the robber in this context, and present upper and lower bounds and exact values, some involving various domination parameters, for an array of graph classes, including paths, cycles, trees, chordal graphs, high girth graphs, and cop-win graphs, as well as graph products.…
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Taxonomy
TopicsAdvanced Graph Theory Research · Cellular Automata and Applications · graph theory and CDMA systems
