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Two-player pebbling on diameter 2 graphs

Author

Listed:
  • Garth Isaak

    (Lehigh University)

  • Matthew Prudente

    (Alvernia University)

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.

Suggested Citation

  • Garth Isaak & Matthew Prudente, 2021. "Two-player pebbling on diameter 2 graphs," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(2), pages 581-596, June.
    • Handle: RePEc:spr:jogath:v:50:y:2021:i:2:d:10.1007_s00182-021-00766-0
    DOI: 10.1007/s00182-021-00766-0
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