منابع مشابه
On k-planar crossing numbers
The k-planar crossing number of a graph is the minimum number of crossings of its edges over all possible drawings of the graph in k planes. We propose algorithms and methods for k-planar drawings of general graphs together with lower bound techniques. We give exact results for the k-planar crossing number ofK2k+1,q , for k 2.We prove tight bounds for complete graphs.We also study the rectiline...
متن کاملOn the Crossing Number of Almost Planar Graphs
If G is a plane graph and x, y ∈ V (G), then the dual distance of x and y is equal to the minimum number of crossings of G with a closed curve in the plane joining x and y. Riskin [7] proved that if G0 is a 3connected cubic planar graph, and x, y are its vertices at dual distance d, then the crossing number of the graph G0 + xy is equal to d. Riskin asked if his result holds for arbitrary 3-con...
متن کاملvertex centered crossing number for maximal planar graph
the crossing number of a graph is the minimum number of edge crossings over all possible drawings of in a plane. the crossing number is an important measure of the non-planarity of a graph, with applications in discrete and computational geometry and vlsi circuit design. in this paper we introduce vertex centered crossing number and study the same for maximal planar graph.
متن کاملCrossing and Weighted Crossing Number of Near-Planar Graphs
A nonplanar graph G is near-planar if it contains an edge e such that G− e is planar. The problem of determining the crossing number of a near-planar graph is exhibited from different combinatorial viewpoints. On the one hand, we develop min-max formulas involving efficiently computable lower and upper bounds. These min-max results are the first of their kind in the study of crossing numbers an...
متن کاملOn the Crossing Number of K{m, n}
The best lower bound known on the crossing number of the complete bipartite graph is : cr(Km,n) ≥ (1/5)(m)(m − 1)bn/2cb(n − 1)/2c In this paper we prove that: cr(Km,n) ≥ (1/5)m(m − 1)bn/2cb(n − 1)/2c + 9.9 × 10−6m2n2 for sufficiently large m and n.
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2019
ISSN: 0012-365X
DOI: 10.1016/j.disc.2018.11.020