Connected even factors in the square of essentially 2-edge connected graphs

TL;DR

This paper investigates the existence of connected even factors with bounded maximum degree in the square of essentially 2-edge connected graphs, proving their existence under certain conditions and highlighting limitations in the general case.

Contribution

The paper establishes conditions under which the square of essentially 2-edge connected graphs contains connected even factors with maximum degree at most 4, and shows limitations in the general case.

Findings

Existence of connected even factors with max degree ≤ 4 in certain graph squares

Counterexamples showing no bounded degree connected even factors in general

Conditions under which such factors are guaranteed

Abstract

In this paper we prove that the square of an essentially 2-edge connected graph with an additional property has a connected even factor with maximum degree at most 4. Moreover we show that, in general, the square of essentially 2-edge connected graph does not contain a connected even factor with bounded maximum degree.