Minimum degree, independence number and pseudo [2,b]-factors in graphs

TL;DR

This paper establishes a sharp upper bound on the number of edges or vertices in a pseudo [2,b]-factor of a graph, linking minimum degree and independence number to the structure of such factors.

Contribution

It provides a new upper bound for the number of small components in pseudo [2,b]-factors, connecting graph parameters like degree and independence number.

Findings

Bound is sharp for certain graph classes

Connects minimum degree to pseudo [2,b]-factor structure

Provides structural insights into graph components

Abstract

A pseudo [2,b]-factor of a graph G is a spanning subgraph in which each component C on at least three vertices is a [2,b]-graph. The main contibution of this paper, is to give an upper bound to the number of components that are edges or vertices in a pseudo [2,b]-factor of a graph G. This bound is sharp.