Star subdivisions and connected even factors in the square of a graph

TL;DR

This paper proves that under certain conditions on induced subgraphs, the square of a graph contains a connected even factor with bounded maximum degree, extending previous results in graph theory.

Contribution

It introduces new conditions involving star subdivisions that guarantee the existence of connected even factors in the square of a graph.

Findings

If every induced S(K_{1, 2s+1}) has at least 3 edges in a block of degree at most two, then G^2 has a [2,2s]-factor.

Extends previous results by Hendry and Vogler, and Abderrezzak et al.

Provides new insights into the structure of graph squares and their factors.

Abstract

For any positive integer $s$, a $[2,2s]$-factor in a graph $G$ is a connected even factor with maximum degree at most $2s$. We prove that if every induced $S(K_{1, 2s+1})$ in a graph $G$ has at least 3 edges in a block of degree at most two, then $G^2$ has a $[2,2s]$-factor. This extends the results of Hendry and Vogler and of Abderrezzak et al.