On the structure of graphs excluding $K_{4}$, $W_{4}$, $K_{2,4}$ and one other graph as a rooted minor

TL;DR

This paper provides structural characterizations of graphs that exclude certain rooted minors, specifically $K_{4}$, $W_{4}$, $K_{2,4}$, and a graph called $L$, enhancing understanding of their structural properties.

Contribution

It introduces new structural characterizations for graphs excluding specific rooted minors, including $K_{4}$, $W_{4}$, $K_{2,4}$, and $L$, expanding the theory of graph minors.

Findings

Structural characterizations of graphs excluding the specified rooted minors.

Identification of properties preventing the presence of these minors.

Framework for analyzing graphs with forbidden rooted minors.

Abstract

In this paper we give structural characterizations of graphs not containing rooted $K_{4}$, $W_{4}$, $K_{2,4}$, and a graph we call $L$.