Details of talk
|Title||The Oberwolfach Problem|
|Presenter||Barbara Maenhaut (The University of Queensland)|
|Session||Algebra 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 complete 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.