Register for: WIMSIG2017

Details of talk

TitleThe Oberwolfach Problem
PresenterBarbara Maenhaut (The University of Queensland)
Author(s)Barbara Maenhaut
SessionAlgebra and Discrete Mathematics

The Oberwolfach problem is a graph factorisation problem  posed by Ringel in
1967. A factor of a graph $G$ is a spanning subgraph of $G$ and a
factorisation of $G$ is a decomposition of $G$ into edge-disjoint factors. A
factor that is regular of degree
$k$ is called a $k$-factor. If each factor of a factorisation is a $k$-factor,
then the factorisation is
called a $k$-factorisation.
For $n\geq  3$ and $F$ a 2-regular graph of order $n$, the Oberwolfach Problem
OP($F$) asks
for a 2-factorisation of the complete graph on $n$ vertices if $n$ is odd, or
of the
complete graph on $n$ vertices with the edges of a 1-factor removed if $n$ is
even, in which each
2-factor is isomorphic to $F$. The problem has been studied extensively, yet a
solution remains out of reach. In this talk  I will discuss some results on the
problem arising from joint work with Brian Alspach, Darryn Bryant, Daniel
Horsley and Victor Scharaschkin.