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



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.

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