Domino Tile Placing on Graphs

TL;DR

This paper studies the process of placing dimers on graphs, specifically analyzing the distribution of uncovered vertices in a maximal independent edge set on lattice graphs, and proves a central limit theorem for this model.

Contribution

It introduces a CLT for the number of uncovered vertices in a dimer placement process on lattice graphs, advancing understanding of random independent edge sets.

Findings

Proves a CLT for the number of uncovered vertices on $\

The model applies to $\

Abstract

Given a graph $G$ we consider sequentially placing dimers on it, namely choosing a maximal independent subset of edges, i.e. edges that do not share common vertices. We study the number of vertices that do not belong to any edge found in the maximal set. We prove a CLT result for this model in the case when the underlying graph is $\mathbb{Z}^d$.