A matrix description of weakly bipartitive and bipartitive families

TL;DR

This paper provides a matrix-based framework for understanding weakly bipartitive and bipartitive families, which are used to analyze graph decompositions and combinatorial structures.

Contribution

It introduces a novel matrix description of weakly bipartitive and bipartitive families, enhancing the theoretical understanding of these concepts.

Findings

Matrix characterization of bipartitive families

Unified framework for graph decomposition analysis

Simplifies the study of combinatorial structures

Abstract

The notions of weakly bipartitive and bipartitive families were introduced by Montgolfier (2003) as a general tool for studying some decomposition of graphs and other combinatorial structures. In this paper, we give a matrix description of these notions.