StronglyConnected Outerplanar Graphs with Proper Touching Triangle RepresentationsFowler, J. Joseph (2013) StronglyConnected Outerplanar Graphs with Proper Touching Triangle Representations. In: 21st International Symposium, GD 2013, September 2325, 2013 , pp. 155160(Official URL: http://dx.doi.org/10.1007/9783319038414_14). Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/9783319038414_14
AbstractA proper touching triangle representation R of an nvertex planar graph consists of a triangle divided into n nonoverlapping triangles. A pair of triangles are considered to be adjacent if they share a partial side of positive length. Each triangle in R represents a vertex, while each pair of adjacent triangles represents an edge in the planar graph. We consider the problem of determining when a proper touching triangle representation exists for a stronglyconnected outerplanar graph, which is biconnected and after the removal of all degree2 vertices and outeredges, the resulting connected subgraph only has chord edges (w.r.t. the original graph). We show that such a graph has a proper representation if and only if the graph has at most two internal faces (i.e., faces with no outeredges).
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