Biplanar crossing numbers. II. Comparing crossing numbers and biplanar crossing numbers using the probabilistic method

The biplanar crossing number cr2(G) of a graph G is min G 1∪G 2=G{cr(G1) + cr(G2)}, where cr is the planar crossing number. We show that cr2(G) ≤ (3/8)cr(G). Using this result recursively, we bound the thickness by Θ(G) ‐ 2 ≤ Kcr2(G)0.4057 log2n with some constant K. A partition realizing this bound...

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Veröffentlicht in:	Random structures & algorithms 2008-12, Vol.33 (4), p.480-496
Hauptverfasser:	Czabarka, Eva, Sykora, Ondrej, Szekely, Laszlo A, Vrto, Imrich
Format:	Artikel
Sprache:	eng
Schlagworte:	biplanar crossing number crossing number graph drawing thickness
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