Cut Bounds for Some Weighted Graphs

TL;DR

This paper establishes lower bounds for cut sizes in weighted graphs with regular properties, extending previous results from unweighted regular graphs to more general weighted cases.

Contribution

It introduces new lower bound results for cuts in weighted regular graphs and generalizes these bounds to broader classes of graphs.

Findings

Lower bounds for cuts in weighted regular graphs are proven.

Results extend previous unweighted graph bounds to weighted graphs.

Applicable to more general graph classes with regular properties.

Abstract

In communication field, an important issue is to group users and base stations to as many as possible subnetworks satisfying certain interference constraints. These problems are usually formulated as a graph partition problems which minimize some forms of graph cut. Previous research already gave some results about the cut bounds for unweighted regular graph. In this paper, we prove a result about the lower bound for weighted graphs that have some regular properties and show similar results for more general case.