Playing cards with Vizing's demon

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.