Splitting vertices of bipartite graphs preserves de Bruijn-Erd\H{o}s property

TL;DR

This paper proves that repeatedly splitting vertices into twins in bipartite graphs preserves the de Bruijn-Erdős property, contributing to graph theory by extending known properties through a specific graph transformation.

Contribution

It introduces a novel vertex-splitting operation in bipartite graphs and proves the preservation of the de Bruijn-Erdős property under this transformation.

Findings

Splitting vertices into twins preserves the de Bruijn-Erdős property.

The property holds for graphs obtained through iterative vertex splitting.

The result extends understanding of graph properties under vertex transformations.

Abstract

In this note, we prove that every graph obtained from a bipartite graph by iteratively splitting vertices into two adjacent twins has the de Bruijn-Erd\H{o}s property.