An Exploration of Graph Pebbling
Herman Bergwerf
TL;DR
This paper provides a comprehensive overview of graph pebbling, exploring key concepts, recent results, and new ideas, serving as an accessible starting point for beginners and offering novel insights for experts.
Contribution
It offers a thorough survey of graph pebbling techniques, introduces new ideas, and presents recent results, enhancing understanding of pebbling numbers and related conjectures.
Findings
Analysis of pebbling numbers and weight functions
New results on flow networks and hypercubes
Insights into the zero-sum conjecture of Erdős and Lemke
Abstract
The topic of this treatise is a combinatorial technique called Graph Pebbling. We investigate pebbling numbers, weight functions, flow networks, hypercubes, and the zero-sum conjecture of Erd\H{o}s and Lemke. This investigation is a comprehensive starting point for anyone who wants to study graph pebbling for the first time, and also includes some new ideas and results for those who have studied it before. For an introductory video, see: https://www.youtube.com/watch?v=yPzyQ4M1f3c
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Taxonomy
TopicsAlgorithms and Data Compression · Data Management and Algorithms