Playing cards with Vizing's demon
Brian Rabern, Landon Rabern

TL;DR
This paper explores a solitaire game involving a demon rearranging cards, demonstrating how classical graph edge coloring theorems by Kőnig and Vizing can be derived from winning strategies in the game.
Contribution
It introduces a novel game-theoretic approach to understanding fundamental graph edge coloring theorems, linking gameplay strategies to mathematical proofs.
Findings
Winning strategies correspond to edge coloring theorems
Game analysis provides new insights into Kőnig's theorem
Vizing's theorem is derived from the game's structure
Abstract
We analyze a solitaire game in which a demon rearranges some cards after each move. The graph edge coloring theorems of K\H{o}nig (1931) and Vizing (1964) follow from the winning strategies developed.
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Taxonomy
TopicsLimits and Structures in Graph Theory · Artificial Intelligence in Games · Game Theory and Applications
