On Maximum Induced Matching Numbers of Special Grids

TL;DR

This paper investigates the maximum induced matching numbers in specific grid graphs, providing new upper bounds and insights into their combinatorial properties.

Contribution

It introduces new upper bounds for the maximum induced matching numbers of certain grid graphs, advancing understanding of their structural limits.

Findings

Derived upper bounds for specific grid graphs' induced matching numbers

Enhanced understanding of the structural properties of grid graphs

Provided theoretical insights applicable to graph matching problems

Abstract

A subset $M$ of the edge set of a graph $G$ is an induced matching of $G$ if given any two $e_1,e_2 \in M$, none of the vertices on $e_1$ is adjacent to any of the vertices on $e_2$. Suppose that $MIM_G$, a positive integer, is the largest possible size of $M$ in $G$, then, $M$ is the maximum induced matching, $MIM$, of $G$ and $MIM_G$ is the maximum induced matching number of $G$. We obtain some upper bounds for the maximum induced matching numbers of some specific grids.