Characterization of unlabeled radial level planar graphs

  • Authors:
  • J. Joseph Fowler

  • Affiliations:
  • Department of Computer Science, University of Arizona

  • Venue:
  • GD'09 Proceedings of the 17th international conference on Graph Drawing
  • Year:
  • 2009

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Abstract

Suppose that an n-vertex graph has a distinct labeling with the integers {1, . . . ,n}. Such a graph is radial level planar if it admits a crossings-free drawing under two constraints. First, each vertex lies on a concentric circle such that the radius of the circle equals the label of the vertex. Second, each edge is drawn with a radially monotone curve. We characterize the set of unlabeled radial level planar(URLP) graphs that are radial level planar in terms of 7 and 15 forbidden subdivisions depending on whether the graph is disconnected or connected, respectively. We also provide linear-time drawing algorithms for any URLP graph.