Dots and Boxes on Certain Families of Graphs
Vedant Aryan, Alana Palmer, Alexander Skula, Matthew Woolbert, Joshua Zelinsky
TL;DR
This paper explores the game Dots and Boxes on specific graph families, analyzing how the game's strategies and outcomes vary across complete, wheel, and friendship graphs.
Contribution
It provides new insights into Dots and Boxes played on particular graph structures, extending understanding beyond traditional grid-based analysis.
Findings
Characterization of game outcomes on complete graphs
Analysis of strategies on wheel graphs
Results on friendship graph gameplay
Abstract
We investigate the Dots and Boxes game, also known as ``Strings and Coins,'' for certain specific families of graphs. These include complete graphs, wheel graphs, and friendship graphs.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · graph theory and CDMA systems · Graph theory and applications