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COMPGEOM
2006
ACM
14 years 3 months ago
On the maximum number of edges in topological graphs with no four pairwise crossing edges
A topological graph is called k-quasi-planar, if it does not contain k pairwise crossing edges. It is conjectured that for every fixed k, the maximum number of edges in a kquasi-...
Eyal Ackerman
DM
2000
158views more  DM 2000»
13 years 9 months ago
Bipartite Ramsey numbers and Zarankiewicz numbers
The Zarankiewicz number z(s, m) is the maximum number of edges in a subgraph of K(s, s) that does not contain K(m, m) as a subgraph. The bipartite Ramsey number b(m, n) is the lea...
Wayne Goddard, Michael A. Henning, Ortrud R. Oelle...
ENDM
2006
119views more  ENDM 2006»
13 years 9 months ago
The incidence game chromatic number
We introduce the incidence game chromatic number which unifies the ideas of game chromatic number and incidence coloring number of an undirected graph. For kdegenerate graphs with...
Stephan Dominique Andres
ENDM
2008
81views more  ENDM 2008»
13 years 9 months ago
The maximum number of halving lines and the rectilinear crossing number of Kn for n
For n 27 we present exact values for the maximum number h(n) of halving lines and h(n) of halving pseudolines, determined by n points in the plane. For this range of values of n ...
Bernardo M. Ábrego, Silvia Fernández...
JCT
2007
90views more  JCT 2007»
13 years 9 months ago
On the maximum number of edges in quasi-planar graphs
A topological graph is quasi-planar, if it does not contain three pairwise crossing edges. Agarwal et al. [2] proved that these graphs have a linear number of edges. We give a sim...
Eyal Ackerman, Gábor Tardos