k-Quasi-Planar Graphs
نویسنده
چکیده
A topological graph is k-quasi-planar if it does not contain k pairwise crossing edges. A topological graph is simple if every pair of its edges intersect at most once (either at a vertex or at their intersection). In 1996, Pach, Shahrokhi, and Szegedy [16] showed that every n-vertex simple k-quasi-planar graph contains at most O ( n(logn) ) edges. This upper bound was recently improved (for large k) by Fox and Pach [8] to n(logn) . In this note, we show that all such graphs contain at most (n log n)2 c k (n) edges, where α(n) denotes the inverse Ackermann function and ck is a constant that depends only on k.
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