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.
Chapter PDF
Similar content being viewed by others
References
Bachmaier, C., Brandenburg, F.J., Forster, M.: Radial level planarity testing and embedding in linear time. Journal of Graph Algorithms and Applications 9(1), 53–97 (2005)
Brandes, U., Kenis, P., Wagner, D.: Communicating centrality in policy network drawings. IEEE Transactions on Visualization and Computer Graphics 09(2), 241–253 (2003)
Brass, P., Cenek, E., Duncan, C.A., Efrat, A., Erten, C., Ismailescu, D., Kobourov, S.G., Lubiw, A., Mitchell, J.S.B.: On simultaneous graph embedding. Computational Geometry: Theory and Applications 36(2), 117–130 (2007)
Cappos, J., Estrella-Balderrama, A., Fowler, J.J., Kobourov, S.G.: Simultaneous graph embedding with bends and circular arcs. Computational Geometry: Theory and Applications 42(2), 173–182 (2009)
Eades, P., Feng, Q., Lin, X., Nagamochi, H.: Straight-line drawing algorithms for hierarchical graphs and clustered graphs. Algorithmica 44(1), 1–32 (2006)
Estrella-Balderrama, A., Fowler, J.J., Kobourov, S.G.: Characterization of unlabeled level planar trees. In: Kaufmann, M., Wagner, D. (eds.) GD 2006. LNCS, vol. 4372, pp. 367–379. Springer, Heidelberg (2007)
Estrella-Balderrama, A., Fowler, J.J., Kobourov, S.G.: Characterization of unlabeled level planar trees. Computational Geometry: Theory and Applications 42(7), 704–721 (2009)
Fowler, J.J.: Characterization of unlabeled radial level planar graphs. Technical Report TR09-03, University of Arizona (2009), http://ulp.cs.arizona.edu/TR09-03.pdf
Fowler, J.J.: Unlabeled Level Planarity. PhD thesis, University of Arizona (2009), http://ulp.cs.arizona.edu/ulp-thesis.pdf
Fowler, J.J., Kobourov, S.G.: Characterization of unlabeled planar graphs. In: Hong, S.-H., Nishizeki, T., Quan, W. (eds.) GD 2007. LNCS, vol. 4875, pp. 37–49. Springer, Heidelberg (2008)
Jünger, M., Leipert, S.: Level planar embedding in linear time. Journal of Graph Algorithms and Applications 6(1), 67–113 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2010 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Fowler, J.J. (2010). Characterization of Unlabeled Radial Level Planar Graphs. In: Eppstein, D., Gansner, E.R. (eds) Graph Drawing. GD 2009. Lecture Notes in Computer Science, vol 5849. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11805-0_10
Download citation
DOI: https://doi.org/10.1007/978-3-642-11805-0_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-11804-3
Online ISBN: 978-3-642-11805-0
eBook Packages: Computer ScienceComputer Science (R0)