Work

A Note on Hamilton Decompositions of Even-Regular Multigraphs

Year: 2024

Type: article

Abstract: In this note, we prove that every even regular multigraph on $n$ vertices with multiplicity at most $r$ and minimum degree at least $rn/2 + o(n)$ has a Hamilton decomposition. This generalises a result of Vaughan who proved an asymptotic version of the multigraph $1$-factorisation conjecture. We derive our result by proving a more general result which states that dense regular multidigraphs that are robust outexpanders have a Hamilton decomposition. This in turn is derived from the corresponding result of Kühn and Osthus about simple digraphs.

Source: The Electronic Journal of Combinatorics

DOI: 10.37236/12637

Author: Vincent Pfenninger

Institution: University of Birmingham

Language: English

Topic: Limits and Structures in Graph Theory

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: European Commission

Award: G434337789