论文信息 - Monotone drawings of planar graphs

Monotone drawings of planar graphs

Let G be a graph drawn in the plane so that its edges are represented by x-monotone curves, any pair of which cross an even number of times. We show that G can be redrawn in such a way that the x-coordinates of the vertices remain unchanged and the edges become non-crossing straight-line segments.

János Pach | Géza Tóth | J. Pach | G. Tóth

[1] In-kyeong Choi. On straight line representations of random planar graphs , 1992 .

[2] K. Wagner. Bemerkungen zum Vierfarbenproblem. , 1936 .

[3] Xuemin Lin,et al. Straight-Line Drawing Algorithms for Hierarchical Graphs and Clustered Graphs , 1996, Graph Drawing.

[4] W. T. Tutte. Toward a theory of crossing numbers , 1970 .

[5] Ioannis G. Tollis,et al. Graph Drawing , 1994, Lecture Notes in Computer Science.

[6] János Pach,et al. Monotone Drawings of Planar Graphs , 2002, ISAAC.

[7] Robert E. Tarjan,et al. Intersection graphs of curves in the plane , 1976, J. Comb. Theory, Ser. B.

[8] Ch. Chojnacki,et al. Über wesentlich unplättbare Kurven im dreidimensionalen Raume , 1934 .

[9] Grant Cairns,et al. Bounds for Generalized Thrackles , 2000, Discret. Comput. Geom..