How to Embed a Path onto Two Sets of Points
Di Giacomo, Emilio and Liotta, Giuseppe and Trotta, Francesco (2006) How to Embed a Path onto Two Sets of Points. In: Graph Drawing 13th International Symposium, GD 2005, September 12-14, 2005, Limerick, Ireland , pp. 111-116 (Official URL: http://dx.doi.org/10.1007/11618058_11).
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Let R and B be two sets of points such that the points of R are colored red and the points of B are colored blue. Let P be a path such that |R| vertices of P are red and |B| vertices of P are blue. We study the problem of computing a crossing-free drawing of P such that each blue vertex is represented as a point of B and each red vertex of P is represented as a point of R. We show that such a drawing can always be realized by using at most one bend per edge.
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