… Note that for many graphs such as regular graphs and degree bounded graphs, A = O(S2),
and therefore the number of crossings in our drawings are still within O(log2n) from the …

… crossing number; the pair crossing number has strong ties to string graphs, intersection graphs
… In Chapter 10 we look at drawing graphs in a fixed number of planes, a crossing number …

… crossing number, provided that m _> 4n. We also derive a general lower bound on the book
crossing number of any graph and … of any graph with O(rn2/k 2) many edge crossings. This …

… number of edge-crossings over all \( k\)-page book drawings of \( G\). Book crossing numbers
… We are concerned with the \( k\)-page book crossing number of the complete graph \( K_n\)…

… Book crossing numbers have been studied in … book crossing number of the complete graph
Kn. In 1964, Blazek and Koman [4] described k-page book drawings of Kn with few crossings …

… problems have a quite long history in the graph theory community (see, eg, Tutte [20] and …
version of the crossing number problem, where the edges of the underlying graph are required …

… of the crossing number problem, where the edges of the underlying graph are required to be
… ], we will use the notation rectilinear crossing number, cr(G), of a graph G. The vertices of G …

… the crossing number of a graph G and the crossing number of its cone CG, the graph …
the smallest f(k) for which there exists a graph with crossing number at least k and cone with …

… graphs with crossing number … graph has crossing number at most k for fixed k, and if this is
the case, we would like to compute a drawing of the graph in the plane with at most k crossings…

… the crossing number of a graph G and the crossing number of its cone CG, the graph …
the smallest f(k) for which there exists a graph with crossing number at least k and cone with …