K_6 minors in large 6-connected graphs

TL;DR

This paper proves Jorgensen's conjecture that large 6-connected graphs without a K_6 minor have a vertex whose removal results in a planar graph, confirming the conjecture for sufficiently large graphs.

Contribution

The paper establishes the conjecture for all sufficiently large 6-connected graphs, advancing understanding of graph minors and connectivity.

Findings

Confirmed Jorgensen's conjecture for large graphs

Identified a vertex whose removal yields a planar graph

Enhanced knowledge of K_6 minors in highly connected graphs

Abstract

Jorgensen conjectured that every 6-connected graph with no K_6 minor has a vertex whose deletion makes the graph planar. We prove the conjecture for all sufficiently large graphs.