论文信息 - Topological graphs with no self-intersecting cycle of length 4

Topological graphs with no self-intersecting cycle of length 4

Let G be a topological graph on n vertices in the plane, i.e., a graph drawn in the plane with its vertices represented as points and its edges represented as Jordan arcs connecting pairs of points. It is shown that if no two edges of any cycle of length 4 in G cross an odd number of times, then |E(G)|=O(n8/5).

Rom Pinchasi | Rados Radoicic | R. Radoicic | R. Pinchasi

[1] Micha Sharir,et al. Lenses in arrangements of pseudo-circles and their applications , 2004, JACM.

[2] M. Simonovits. Some extremal problems in graph theory , 2004 .

[3] P. Erdős,et al. COLLOQUIA MATHEMATICA SOCIETATIS JÁNOS BOLYAI 4 . COMBINATORIAL THEORY AND ITS APPLICATIONS , 1969 .

[4] Igor Rivin,et al. On some extremal problems in graph theory , 1999 .

[5] M. Sharir,et al. Lenses in arrangements of pseudo-circles and their applications , 2002, SCG '02.

[6] János Pach,et al. Relaxing Planarity for Topological Graphs , 2002, JCDCG.

[7] M. Simonovits,et al. Cube-Supersaturated Graphs and Related Problems , 1982 .

[8] Hisao Tamaki,et al. How to cut pseudo-parabolas into segments , 1995, SCG '95.

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

[10] Hisao Tamaki,et al. How to Cut Pseudoparabolas into Segments , 1998, Discret. Comput. Geom..

[11] Pavel Valtr,et al. A Turán-type Extremal Theory of Convex Geometric Graphs , 2003 .

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

[13] V. Sós,et al. On a problem of K. Zarankiewicz , 1954 .

[14] P. Erdos,et al. Extremal problems in combinatorial geometry , 1996 .

[15] János Pach,et al. Geometric graphs with no self-intersecting path of length three ∗ , 2022 .