$P$-Matchings in Graphs: A Brief Survey with Some Open Problems

TL;DR

This paper surveys various types of matchings in graph theory, highlighting key concepts and open problems to guide future research in the field.

Contribution

It provides a comprehensive overview of different matching variants and presents unresolved questions for further exploration.

Findings

Multiple matching types are systematically discussed

Open problems are identified for future research

The survey consolidates existing knowledge in the field

Abstract

For a graph $G=(V,E),$ a matching $M$ is a set of independent edges. The topic of matchings is well studied in graph theory. In this paper many varieties of matchings are discussed.