# Local Properties that imply Global Cycle Properties

### Marietjie Frick University of South Africa

#### Ortrud Oellermann University of Winnipeg

PDF

Minisymposium: GENERAL SESSION TALKS

Content: We say a graph $G$ has a property ${\cal P}$ \emph{locally} (or $G$ is \emph{locally} $\cal P$) if for every vertex $v$ in $G$, the graph induced by the open neighbourhood $N(v)$ of $G$ has property $\cal P$. For example, a graph $G$ is \emph{locally connected} if $G[N(v)]$ is connected for every vertex $v$ in $G$. We discuss the global cycle structure of locally connected, locally traceable and locally hamiltonian graphs with bounded vertex degree.

Back to all abstracts