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\section{Representing Euler diagrams as graphs}
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\section{Representing Euler diagrams as graphs}
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As the relationships {\em enclosure} and {\pic} are mutually exclusive
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As the relationships {\em enclosure} and {\em pair-wise intersection} are mutually exclusive
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and {\em enclosure} is transitive and {\pic} is not, we can represent
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and {\em enclosure} is transitive and {\em pair-wise intersection} is not, we can represent
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an {\em enclosure} relationship as a directed vertice and
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an {\em enclosure} relationship as a directed vertice and
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{\pic} as non-directed on the same graph.
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{\pic} as non-directed on the same graph.
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Figures \ref{fig:eulerg1} and \ref{fig:eulerg_enc} show euler diagrams with corresponding
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Figures \ref{fig:eulerg1} and \ref{fig:eulerg_enc} show euler diagrams with corresponding
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