The Characterization of planar, 4-connected, K_{2,5}-minor-free graphs

TL;DR

This paper proves that all planar, 4-connected, K_{2,5}-minor-free graphs are precisely the squares of even cycles of length six or more, revealing a specific structural characterization.

Contribution

It provides a complete characterization of a class of graphs by showing they are exactly the squares of certain even cycles, a novel structural insight.

Findings

All such graphs are squares of even cycles of length ≥6.

This class of graphs is characterized by planarity, 4-connectivity, and K_{2,5}-minor-freeness.

The result links graph minors, planarity, and cycle structures.

Abstract

We show that every planar, 4-connected, K2;5-minor- free graph is the square of a cycle of even length at least six.