Hoffmann-Ostenhof's conjecture for traceable cubic graphs

TL;DR

This paper proves Hoffmann-Ostenhof's conjecture for traceable cubic graphs, demonstrating that their edges can be decomposed into a spanning tree, a matching, and cycles, thus confirming the conjecture in this specific case.

Contribution

The paper establishes the validity of Hoffmann-Ostenhof's conjecture specifically for traceable cubic graphs, a significant step in understanding the conjecture's scope.

Findings

Conjecture holds for traceable cubic graphs

Edges can be decomposed into a spanning tree, matching, and cycles in these graphs

Supports broader conjecture validation efforts

Abstract

It was conjectured by Hoffmann-Ostenhof that the edge set of every connected cubic graph can be decomposed into a spanning tree, a matching and a family of cycles. In this paper, we show that this conjecture holds for traceable cubic graphs.