Algorithms for 1-Planar Graphs

[1]  David Eppstein,et al.  Parameterized Complexity of 1-Planarity , 2013, WADS.

[2]  János Pach,et al.  How to draw a planar graph on a grid , 1990, Comb..

[3]  Yusuke Suzuki,et al.  On properties of maximal 1-planar graphs , 2012, Discuss. Math. Graph Theory.

[4]  Vladimir P. Korzhik,et al.  Minimal Obstructions for 1‐Immersions and Hardness of 1‐Planarity Testing , 2013, J. Graph Theory.

[5]  Hiroshi Nagamochi,et al.  An algorithm for constructing star-shaped drawings of plane graphs , 2010, Comput. Geom..

[6]  Giuseppe Liotta,et al.  Straight-Line Drawability of a Planar Graph Plus an Edge , 2015, WADS.

[7]  Tomás Madaras,et al.  The structure of 1-planar graphs , 2007, Discret. Math..

[8]  André Raspaud,et al.  Acyclic colouring of 1-planar graphs , 2001, Discret. Appl. Math..

[9]  Roberto Tamassia,et al.  On-line maintenance of triconnected components with SPQR-trees , 1996, Algorithmica.

[10]  Giuseppe Liotta,et al.  A Linear-Time Algorithm for Testing Outer-1-Planarity , 2013, Algorithmica.

[11]  Giuseppe Liotta,et al.  Fáry's Theorem for 1-Planar Graphs , 2012, COCOON.

[12]  Hiroshi Nagamochi,et al.  A linear-time algorithm for testing full outer-2-planarity , 2019, Discret. Appl. Math..

[13]  Alexander Grigoriev,et al.  Algorithms for Graphs Embeddable with Few Crossings per Edge , 2005, Algorithmica.

[14]  Hiroshi Nagamochi,et al.  Re-embedding a 1-Plane Graph into a Straight-Line Drawing in Linear Time , 2016, GD.

[15]  Franz-Josef Brandenburg,et al.  Journal of Graph Algorithms and Applications 1-planarity of Graphs with a Rotation System 68 Auer Et Al. 1-planarity of Graphs with a Rotation System , 2022 .

[16]  János Pach,et al.  Graphs drawn with few crossings per edge , 1997, Comb..

[17]  Yusuke Suzuki.  Re-embeddings of Maximum 1-Planar Graphs , 2010, SIAM J. Discret. Math..

[18]  Xin Zhang,et al.  On edge colorings of 1-planar graphs , 2011, Inf. Process. Lett..

[19]  Carsten Thomassen,et al.  Rectilinear drawings of graphs , 1988, J. Graph Theory.

[20]  Christian Bachmaier,et al.  Outer 1-Planar Graphs , 2016, Algorithmica.

[21]  Bojan Mohar,et al.  Adding One Edge to Planar Graphs Makes Crossing Number and 1-Planarity Hard , 2012, SIAM J. Comput..

[22]  G. Ringel.  Ein Sechsfarbenproblem auf der Kugel , 1965 .

[23]  Yusuke Suzuki,et al.  Optimal 1-planar graphs which triangulate other surfaces , 2010, Discret. Math..

[24]  Giuseppe Liotta,et al.  A linear time algorithm for testing maximal 1-planarity of graphs with a rotation system , 2013, Theor. Comput. Sci..