Characterising graphs with no subdivision of a wheel of bounded diameter

TL;DR

This paper characterizes graphs that contain a bounded subdivision of a wheel using a specific type of graph decomposition based on locality and width.

Contribution

It establishes a precise equivalence between the existence of an r-bounded wheel subdivision and a particular graph decomposition.

Findings

Graphs with an r-bounded wheel subdivision are characterized by a locality r and width at most two decomposition.

Provides a new structural characterization of wheel subdivisions in graphs.

Bridges the concepts of subdivisions and graph decompositions in graph theory.

Abstract

We prove that a graph has an r-bounded subdivision of a wheel if and only if it does not have a graph-decomposition of locality r and width at most two.