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Star-Shaped Drawings of Graphs with Fixed Embedding and Concave Corner Constraints

  • Seok-Hee Hong
  • Hiroshi Nagamochi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5092)

Abstract

A star-shaped drawing of a graph is a straight-line drawing such that each inner facial cycle is drawn as a star-shaped polygon, and the outer facial cycle is drawn as a convex polygon. In this paper, given a biconnected planar graph G with fixed plane embedding and a subset A of corners of G, we consider the problem of finding a star-shaped drawing D of G such that only corners in A are allowed to become concave corners in D. We first characterize a necessary and sufficient condition for a subset A of corners to admit such a star-shaped drawing D. Then we present a linear time algorithm for finding such a star-shaped drawing D. Our characterization includes Thomassen’s classical characterization of biconnected plane graphs with a prescribed boundary that have convex drawings.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Seok-Hee Hong
    • 1
  • Hiroshi Nagamochi
    • 2
  1. 1.School of Information TechnologiesUniversity of Sydney 
  2. 2.Department of Applied Mathematics and PhysicsKyoto University 

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