On lower bounds for the matching number of subcubic graphs

TL;DR

This paper characterizes the set of linear bounds for the matching number in connected subcubic graphs, identifying conditions on vertex degree distributions that guarantee such bounds.

Contribution

It provides a complete description of the triples (a,b,c) that define universal lower bounds for the matching number based on degree counts in subcubic graphs.

Findings

Identifies all triples (a,b,c) with a constant K that bound the matching number from below.

Establishes a complete characterization of degree-based lower bounds for matching numbers.

Provides a framework for understanding bounds in terms of degree distributions in subcubic graphs.

Abstract

We give a complete description of the set of triples (a,b,c) of real numbers with the following property. There exists a constant K such that a n_3 + b n_2 + c n_1 - K is a lower bound for the matching number of every connected subcubic graph G, where n_i denotes the number of vertices of degree i for each i.