Path connectivity of line graphs

TL;DR

This paper investigates the path connectivity properties of line graphs, extending Dirac's classical results on graph connectivity to a generalized setting involving path connectivity.

Contribution

The paper explores the path connectivity of line graphs, providing new insights and generalizations related to Dirac's theorem and the concept of path k-connectivity.

Findings

Analysis of path connectivity in line graphs

Generalization of Dirac's theorem to path k-connectivity

New bounds or properties for path connectivity in line graphs

Abstract

Dirac showed that in a $(k-1)$-connected graph there is a path through each $k$ vertices. The path $k$-connectivity $\pi_k(G)$ of a graph $G$, which is a generalization of Dirac's notion, was introduced by Hager in 1986. In this paper, we study path connectivity of line graphs.