On a specific problem of partition of graph

TL;DR

This paper investigates a specific graph partition problem, establishing a lower bound on the number of crossing edges for graphs that can be partitioned into small components.

Contribution

It introduces a new lower bound on crossing edges in 2-partitions of graphs that decompose into small subgraphs.

Findings

Established a lower bound for crossing edges in 2-partitions

Applicable to graphs decomposable into small subgraphs

Provides insights into graph partitioning constraints

Abstract

In this short article, we consider a problem about $2$-partition of the vertices of a graph. If a graph admits such a partition into some 'small' graphs, then the number of edges cross an arbitrary cut of the graph $e(S,S^{c})$ has a nice lower bound.