نتایج جستجو برای: crossing number
تعداد نتایج: 1191109 فیلتر نتایج به سال:
Tanglegrams are special graphs that consist of a pair of rooted binary trees with the same number of leaves, and a perfect matching between the two leaf-sets. These objects are of use in phylogenetics and are represented with straightline drawings where the leaves of the two plane binary trees are on two parallel lines and only the matching edges can cross. The tangle crossing number of a tangl...
The crossing number of a graph is the minimum number of edge intersections in a plane drawing of a graph, where each intersection is counted separately. If instead we count the number of pairs of edges that intersect an odd number of times, we obtain the odd crossing number. We show that there is a graph for which these two concepts differ, answering a well-known open question on crossing numbe...
We prove that the crossing number of C4 X C4 is 8.
The monotone crossing number of G is defined as the smallest number of crossing points in a drawing of G in the plane, where every edge is represented by an x-monotone curve, that is, by a connected continuous arc with the property that every vertical line intersects it in at most one point. It is shown that this parameter can be strictly larger than the classical crossing number cr(G), but it ...
The minor crossing number of a graph G, mcr(G), is defined as the minimum crossing number of all graphs that contain G as a minor. We present some basic properties of this new minor-monotone graph invariant. We give estimates on mcr for some important graph families using the topological structure of graphs satisfying mcr(G) ≤ k.
We define the crossing number, a natural invariant in topological graph theory, and survey general results on the crossing number in the Euclidean plane. We also discuss progress on conjectures for two particular cases: complete bipartite graphs and complete graphs. Finally, we show some applications of the crossing number to problems in incidence geometry and VLSI chip design.
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