Local Properties that imply Global Cycle Properties
Marietjie Frick
University of South Africa
Susan van Aardt
University of South Africa
Johan de Wet
University of South Africa
Ortrud Oellermann
University of Winnipeg
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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.