Two-player pebbling on diameter 2 graphs

Garth Isaak and Matthew Prudente ()
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Garth Isaak: Lehigh University
Matthew Prudente: Alvernia University

International Journal of Game Theory, 2021, vol. 50, issue 2, No 12, 596 pages

Abstract: Abstract A pebbling move refers to the act of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The goal of graph pebbling is: Given an initial distribution of pebbles, use pebbling moves to reach a specified goal vertex called the root. The pebbling number of a graph $$\pi (G)$$ π ( G ) is the minimum number of pebbles needed so every distribution of $$\pi (G)$$ π ( G ) pebbles can reach every choice of the root. We introduce a new variant of graph pebbling, a game between two players. One player aims to move a pebble to the root and the other player aims to prevent this. We show configurations of various classes of graphs for which each player has a winning strategy. We will characterize the winning player for a specific class of diameter two graphs.

Keywords: Graph theory; Graph pebbling; Game theory (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s00182-021-00766-0

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