k-Colored Point-Set Embeddability of Outerplanar Graphs

  • Emilio Di Giacomo
  • Walter Didimo
  • Giuseppe Liotta
  • Henk Meijer
  • Francesco Trotta
  • Stephen K. Wismath
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4372)


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 V 0, ⋯ , V k − 1, and k disjoint sets S 0, ⋯ , S k − 1 of points in the plane with |V i | = |S i | (i ∈ {0, ⋯ , k − 1}). The desired output is a planar drawing such that the vertices of V i are mapped onto the points of S i 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.


Planar Graph Hamiltonian Cycle Simple Cycle Outerplanar Graph External Face 
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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Emilio Di Giacomo
    • 1
  • Walter Didimo
    • 1
  • Giuseppe Liotta
    • 1
  • Henk Meijer
    • 2
  • Francesco Trotta
    • 1
  • Stephen K. Wismath
    • 3
  1. 1.Dip. di Ingegneria Elettronica e dell’Informazione, Università degli Studi di Perugia 
  2. 2.Department of Computing and Information Science, Queen’s University 
  3. 3.Department of Mathematics and Computer Science, University of Lethbridge 

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