Geodesic
k-colored Point-set Embeddability of Outerplanar Graphs
Journal of Graph Algorithms and Applications, Special Issue on Selected Papers from the Fourteenth International Symposium on Graph Drawing, GD 2006 , Tome 12 (2008) no. 1, pp. 29-49.

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This paper addresses the problem of designing drawing algorithms that receive as input a planar graph G, a partitioning of the vertices of G into k different semantic categories V0,..., Vk−1, and k disjoint sets S0, ..., Sk−1 of points in the plane with |Vi|=|Si| (i ∈ {0, ...,k−1}). The desired output is a planar drawing such that the vertices of Vi are mapped onto the points of Si and such that the curve complexity of the edges (i.e. the number of bends along each edge) is kept small. Particular attention is devoted to outerplanar graphs, for which lower and upper bounds on the number of bends in the drawings are established. 
@article{JGAA_2008_12_1_a2,
     author = {Emilio Di Giacomo and Walter Didimo and Giuseppe Liotta and Henk Meijer and Francesco Trotta and Stephen Wismath},
     title = {k-colored {Point-set} {Embeddability} of {Outerplanar} {Graphs}},
     journal = {Journal of Graph Algorithms and Applications},
     pages = {29--49},
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     volume = {12},
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     year = {2008},
     doi = {10.7155/jgaa.00158},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00158/}
}
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Emilio Di Giacomo; Walter Didimo; Giuseppe Liotta; Henk Meijer; Francesco Trotta; Stephen Wismath. k-colored Point-set Embeddability of Outerplanar Graphs. Journal of Graph Algorithms and Applications, 
							Special Issue on Selected Papers from the Fourteenth International Symposium on Graph Drawing, GD 2006
					, Tome 12 (2008) no. 1, pp. 29-49. doi : 10.7155/jgaa.00158. http://geodesic.mathdoc.fr/articles/10.7155/jgaa.00158/

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