Covering a graph by forests and a matching

TL;DR

This paper proves a new decomposition theorem for graphs with bounded fractional arboricity, showing they can be split into multiple forests and a matching, advancing understanding of graph structure and decompositions.

Contribution

It establishes a novel decomposition result for graphs with fractional arboricity at most $k + 1/(3k+2)$ into $k$ forests and a matching, extending prior work.

Findings

Graphs with fractional arboricity ≤ $k + 1/(3k+2)$ can be decomposed into $k$ forests and a matching.

The result generalizes previous arboricity decompositions to fractional cases.

Provides a new structural insight into graph decompositions based on fractional arboricity.

Abstract

We prove that for any positive integer $k$, the edges of any graph whose fractional arboricity is at most $k + 1/(3k+2)$ can be decomposed into $k$ forests and a matching.