All longest cycles intersect in partial 3-trees

TL;DR

This paper proves that in 2-connected partial 3-trees, all longest cycles share at least one common vertex, revealing a structural property of these graphs.

Contribution

It establishes a new intersection property of longest cycles specifically within 2-connected partial 3-trees, a class of graphs.

Findings

All longest cycles intersect in 2-connected partial 3-trees.

The intersection property holds for this class of graphs.

Provides insights into the cycle structure of partial 3-trees.

Abstract

We show that all longest cycles intersect in 2-connected partial 3-trees.