On the maximum number of edges in planar graphs of bounded degree and matching number

TL;DR

This paper establishes the maximum number of edges in planar graphs based on their maximum degree and matching number, providing a precise relationship between these parameters.

Contribution

It introduces a formula linking maximum edges in planar graphs to degree and matching constraints, advancing understanding of graph density limits.

Findings

Derived the maximum edge count as a function of degree and matching number.

Provided tight bounds for planar graphs with given parameters.

Enhanced theoretical understanding of planar graph density constraints.

Abstract

We determine the maximum number of edges that a planar graph can have as a function of its maximum degree and matching number.