How to embed a path onto two sets of points

Authors:
Emilio Di Giacomo;Giuseppe Liotta;Francesco Trotta
Affiliations:
Dipartimento di Ingegneria Elettronica e dell’Informazione, Università degli Studi di Perugia;Dipartimento di Ingegneria Elettronica e dell’Informazione, Università degli Studi di Perugia;Dipartimento di Ingegneria Elettronica e dell’Informazione, Università degli Studi di Perugia
Venue:
GD'05 Proceedings of the 13th international conference on Graph Drawing
Year:
2005

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Abstract

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.