On normal odd partitions in cubic graphs

TL;DR

This paper explores the concept of normal partitions in cubic graphs, where edges are divided into trails with specific end-vertex properties, providing new insights and open problems in this area.

Contribution

It introduces the notion of normal partitions in cubic graphs and presents initial results and open problems related to their properties.

Findings

Initial results on the existence of normal partitions

Identification of open problems in the area

Framework for further research on trail partitions

Abstract

A normal partition of the edges of a cubic graph is a partition into trails (no repeated edge) such that each vertex is the end vertex of exactly one trail of the partition. We investigate this notion and give some results and problems.