2-walks in 2-tough 2k2-free graphs

TL;DR

This paper proves that every 2-tough 2$K_2$-free graph contains a 2-walk, advancing understanding of graph toughness and specific structural properties.

Contribution

It establishes the existence of a 2-walk in 2-tough 2$K_2$-free graphs, a new result linking toughness and graph structure.

Findings

Existence of 2-walk in 2-tough 2$K_2$-free graphs

Strengthens the connection between graph toughness and walk properties

Provides a new structural insight into 2$K_2$-free graphs

Abstract

In this paper, we prove that in every 2-tough 2$K_2$-free graph, there is a 2-walk.