Hoffmann-Ostenhof's conjecture for claw-free cubic graphs

TL;DR

This paper proves Hoffmann-Ostenhof's conjecture for claw-free cubic graphs, demonstrating that their edges can be decomposed into a spanning tree, a matching, and a 2-regular subgraph.

Contribution

The paper establishes the validity of Hoffmann-Ostenhof's conjecture specifically for claw-free cubic graphs, a significant subclass of cubic graphs.

Findings

Conjecture holds for claw-free cubic graphs

Edge decomposition into spanning tree, matching, and 2-regular subgraph confirmed

Advances understanding of graph decompositions in special graph classes

Abstract

Hoffmann-Ostenhof's Conjecture states that states that the edge set of every connected cubic graph can be decomposed into a spanning tree, a matching and a $2$-regular subgraph. In this paper, we show that the conjecture holds for claw-free cubic graphs.