A game generalizing Hall's theorem

TL;DR

This paper introduces a new game-theoretic framework that generalizes Hall's theorem, providing a broader characterization of winning strategies in two-player games and deriving Vizing's edge coloring theorem as a special case.

Contribution

It presents a novel generalization of Hall's theorem through a game-theoretic approach, connecting it to Vizing's edge coloring theorem.

Findings

Characterization of initial positions with winning strategies

Generalization of Hall's theorem

Derivation of Vizing's edge coloring theorem

Abstract

We characterize the initial positions from which the first player has a winning strategy in a certain two-player game. This provides a generalization of Hall's theorem. Vizing's edge coloring theorem follows from a special case.